The field for the 41st Joe Hartmann Diamond Classic will be announced Sunday night.
Haddonfield, St. Augustine, Pennsville, and Northern Burlington appear to have locked up automatic bids.
Gloucester Catholic has no chance of one.
The Rams, who were moved from the Tri-County's Diamond Division to the Royal for the purposes of the Diamond Classic's automatic-bid arrangement, won't play the minimum of six "division" games before the cutoff.
But the Rams, who rose to No. 3 in The Inquirer's South Jersey rankings after Sunday's 11-1 win over then-No. 2 St. Augustine, almost certainly will make the field with an at-large berth.
Haddonfield (5-1 division record) had already clinched a berth but put an exclamation point on its return to the prestigious tournament with a 16-10 victory over closest pursuer Sterling on Tuesday.
Pennsville, No. 2 in the rankings, went to 6-0 in the Tri-County Classic and 13-0 overall with a 15-0 victory over Wildwood on Tuesday.
Northern Burlington, the No. 5 team, likely locked up the Burlco Liberty berth with a 7-4 win over Rancocas Valley on Tuesday. NBC is 6-1 in the division and doesn't have another game scheduled before Saturday's cutoff.
No. 4 St. Augustine went to 6-0 in the division with a 12-4 win over Hammonton on Tuesday.
The Joe Hartmann Diamond Classic is a 16-team tournament scheduled to start with eight games at four sites on May 10 and culminate with the title game May 18 at Eastern. Washington Township is the defending champion.
Under the tournament's format, 10 teams will receive automatic bids as division leaders and six teams will receive at-large bids.
The at-large bids will be based on the recommendations of a committee of sportswriters who cover South Jersey baseball.
This week will be crucial for teams jockeying for berths, although the weather could have a big impact.
Here's a look at the races for the 10 division automatic bids:
Burlington Liberty: Northern Burlington.
Burlington Freedom: The winner of Friday's game between host Maple Shade (7-1) and New Egypt (5-1) could get the berth, although Riverside (4-1) remains alive.
Olympic American: Washington Township (6-1) and Cherokee (6-1) are tied for the top spot.
Olympic National: Paul VI is 5-0, and No. 1 Bishop Eustace is 5-1. They were supposed to play Wednesday, but the game already has been postponed to Saturday at 2 p.m. at the Crusaders' field. Camden Catholic (4-2) is alive.
Colonial Liberty: Haddonfield.
Colonial Patriot: Woodbury (4-1) and Audubon (5-1) are the contenders.
Tri-Co Classic: Pennsville.
Tri-Co Royal: Clearview (5-2) has Williamstown (3-2) on Wednesday and Kingsway (3-2) on Friday. GCIT (3-2) is scheduled to play Delsea Wednesday.
Cape-American: St. Augustine.
Cape-National: Buena (8-1), Cedar Creek (7-1), and Ocean City (6-2) are jostling for this berth. Ocean City is scheduled to play at Cedar Creek on Thursday.