UPDATED a few times: A number of players are out of the Re-Entry Draft pool. Some were taken in the first stage of the process, some were traded, and some negotiated new contracts. I have noted those changes below and will continue to update this post as more transactions are announced.

The Major League Soccer Re-Entry Draft is a two-stage process which is used to grant a form of free agency to players who have spent a qualifying amount of time in the league.

A player who is either out of contract or who has had an option year declined, and who has the qualifying time played (it varies by age) is eligible to be selected. If the player passes through both stages, he becomes available to any club within MLS on a first-come, first-served basis.

It is not pure free agency, but within the league's single-entity structure, it is a close approximation. And as with all roster rules in MLS, it is collectively bargained by the league and the players' union.

The rules on how teams must deal with contracts of drafted players are a bit byzantine. MLS' website has an explanation here. The rules for player eligiblity are here about two-thirds of the way down the page.

The key point in the process is that there is a lot more freedom to negotiate new deals with players selected in the second stage of the process than the first. For this reason, the first stage usually passes without much action, but the second stage can get quite busy.

You might remember that the Union landed Conor Casey this way. They selected him in the second stage of the 2012 Re-Entry Draft, and negotiated his salary down from $400,000 to $175,000.

This year's pool of eligible players has quite a bit of talent in it, as you'll see from the list below.

Which players would you like to see the Union pursue? I've added in the salary figures from this past season to give you some more context. And I've noted some players in italics who I think would help the Union.

Here are the players currently eligible for the second stage of the Re-Entry Draft:

Chicago Fire

M Corben Bone ($49,000.00, option declined) (drafted by the Philadelphia Union in Stage One)
D Shaun Francis ($46,500.00, option declined)
M Joel Lindpere ($205,000.00, option declined)
F Daniel Paladini ($91,103.25, option declined) (traded to Columbus)
M Logan Pause ($197,833.33, option declineed (negotiating new contract)
M Chris Rolfe ($248,333.33, option declined) 1 (negotiating new contract)
F Maicon Santos ($164,433.33, option declined)
M Wells Thompson ($113,125.00, out of contract)
M Michael Videira ($47,125.00, option declined)

1 - He'd be a good playmaker at the top of the midfield, or a withdrawn forward behind a pure finisher.
Chivas USA

D Ante Jazic ($132,187.50, out of contract)
D Steve Purdy ($80,004.00, option declined)
M Josue Soto ($35,125.00, option declined)

Colorado Rapids

GK Steward Ceus ($70,333.33, option declined)
M Brian Mullan ($170,335.00, option declined)
D Jamie Smith ($46,500.00, option declined)

Columbus Crew

D Danny O'Rourke ($175,000.00, option declined)
M Konrad Warzycha ($46,500.00, option declined)

D.C. United

M Dwayne De Rosario ($645,333.33, option declined)
D James Riley ($145,750.00, option declined)
F Carlos Ruiz ($75,000.00, option declined)
M Marcelo Saragosa ($110,000.00, option declined)
M John Thorrington ($150,000.00, option declined) (negotiating new contract)
D Daniel Woolard (option declined)

FC Dallas

F Kenny Cooper ($342,500.00, option declined) 1
M David Ferreira ($730,000.00, option declined) 2

D Ugo Ihemelu ($200,000.00, option declined)

1 - It's a big price tag that would have to be negotiated down in the second stage of the draft. But he has given the Union nightmares over the years, and John Hackworth knows him well.
2 - Another steep price tag, and he's had some serious injuries over the last few years. But it's hard to totally overlook a former MLS MVP who's one of the league's best playmakers. 

Houston Dynamo

D Bobby Boswell ($220,000.00, out of contract) (drafted by D.C. United in Stage One)
M Calen Carr ($94,588.00, out of contract)
D Michael Chabala ($57,508.00, option declined) (negotiating new contract)
M Alex Dixon ($54,612.50, option declined)
F Cam Weaver ($108,406.67, option declined)

Los Angeles Galaxy

M Colin Clark ($80,000.00, option declined)
M Laurent Courtois ($46,500.00, option declined)
D Sean Franklin ($248,333.33, option declined) (drafted by D.C. United in Stage One)
M Pablo Mastroeni ($200,000.00, out of contract) (retired)

Montréal Impact

M Sinisa Ubiparipovic ($57,750.00, option declined)

New England Revolution

D Kevin Alston ($194,000.00, out of contract)
F Chad Barrett ($110,709.17, option declined)
F Ryan Guy ($48,510.00, option declined)
M Clyde Simms ($90,833.33, option declined)
M Juan Toja ($295,000.00, option declined)

New York Red Bulls

F Andre Akpan ($67,595.00, out of contract) (signed new contract)
M Brandon Barklage ($67,595.00, option declined) 1
F Fabián Espindola ($150,000.00, option declined)
GK Kevin Hartman ($54,000.00, option declined) (retired)
D Heath Pearce ($340,736.00, out of contract) 2

1 - He might want a starting job, and he might not get it with Brian Carroll anchoring the midfield. But he's a workhorse and he's cheap, and he could play alongside Carroll in the bottom of a midfield triangle.
2 - It's a lot of money, but he's a left back who would bring veteran experience to a Union locker room that needs both of those things. Negotiate the number down in the second stage and he'd fit right in at PPL Park.

Philadelphia Union

D Chris Albright ($75,000.00, out of contract) (retired)

Portland Timbers

D David Horst ($70,000.00, option declined) 1 (traded to Houston Dynamo)
D Ryan Miller (option declined)

1 - He'd be at the top of my shopping list. The native of Pine Grove, Pa. (just off I-81 between Pottsville and Lebanon) is a central defender, and the Union really need depth at that position. He's been injury-prone, but for that money it's a risk worth taking.
Real Salt Lake

M Yordany Álvarez ($46,500, option declined)
M Brandon McDonald ($273,250.00, ,option declined)
GK Josh Saunders ($95,250.00, option declined)
M Khari Stephenson ($81,958.33, option declined) 1

1 - Not at the top of my list, but he'd bring midfield depth - and he can really hammer a shot from long range. The Union could use a little of that kind of spice.

Seatle Sounders

D Marc Burch ($75,000.00, option declined) 1 (drafted by Colorado Rapids in Stage One)
GK Josh Ford ($46,500.00, option declined) (signed to a new contract)
M Blair Gavin ($35,125.00, option declined)
M Mauro Rosales ($225,000.00, option declined) (traded to Chivas USA and signed to a new deal)
M Steve Zakuani ($233,000.00, out of contract) 2 (drafted by Portland Timbers in Stage One)

1 - Another good option at left back, and a lot cheaper than Pearce. Seattle didn't announce its eligible players until right before the leaguewide list was unveiled, whereas Pearce's status had been known for a while. So I was a bit surprised to see Burch's name on here. But if the Sounders are willing to let him go, I'd make a run at him.
2 - Perhaps the highest-profile name on this list. The left winger has had to deal with some major injuries over the last few seasons, but if he can get his speed back, almost every coach in MLS will want him. Here's an example of why - but you'll see that it came from the 2010 season. I can see Zakuani fitting with the Union, but it would definitely be a gamble.
San Jose Earthquakes

D Nana Attakora ($61,665.00, option declined)
M Mehdi Ballouchy ($152,006.00, out of contract) 1
M Dan Gargan ($88,000.00, option declined)
GK Evan Newton ($46,500.00, option declined)

1 - It's hard for me to believe that Ballouchy has played eight seasons in MLS already. It doesn't feel like it was so long ago that he was one of the league's top young playmakers. He's been played out of position by a lot of coaches in his MLS career, and he probably isn't starting-caliber anymore. But I can't help wondering if he might have a bit left in the tank.

Toronto FC

F Justin Braun ($114,700.00, out of contract)
M Bobby Convey ($215,000.00, option declined) 1 (traded to the New York Red Bulls)

1 - The rumor going around is TFC want to re-sign the Philadelphia native for a lower salary. If they can't get a deal done, there will be a fair number of Union fans wondering if it's time for the Penn Charter product to come home. I've watched his entire pro career pretty closely, and there's no doubt he's a shadow of his former self. But once upon a time, you could have claimed he was the most talented player the city has ever produced. After all, he's a left-sided player, and that's where the Union need the most help.
Vancouver Whitecaps

GK Joe Cannon ($189,916.67, option declined, likely to retire)
F Tommy Heinemann ($51,975.00, option declined) (opted out, negotiating new contract)
F Corey Hertzog ($60,670.67, option declined) 1
GK Brad Knighton ($68,600.00, option declined) (traded to New England)

1 - The Reading native and Penn State product would give the Union some depth at forward, and he'd come cheap. I still remember talking to him when he was drafted by the Red Bulls in 2011. He wanted to come to Philadelphia. Now might be the time to make it happen.