After signing two notable free agents within a seven-day span in December, and with the franchise-record payroll closing in on luxury-tax territory, Phillies officials were waiting to scoop up veteran pitchers who, for whatever reason, must settle for minor-league contracts.

It seems that market is finally percolating.

The Phillies will take fliers on former big-league closers Drew Storen and Bud Norris, multiple sources said Tuesday. Neither right-hander pitched in the majors last season, but both will receive non-roster invitations to camp next month in Clearwater, Fla., and a chance to win jobs in a bullpen that is flush with opportunity.

Storen, 32, hasn’t pitched in the majors since 2017. At his peak, he posted a 3.02 ERA and 95 saves for the Washington Nationals from 2010-15. He got traded to the Toronto Blue Jays before the 2016 season, then ping-ponged to the Seattle Mariners and Cincinnati Reds over the next two years. His career stalled in 2017 after he underwent Tommy John elbow surgery and missed the 2018 season.

This marks the second consecutive year in which Storen signed a minor-league contract. He attempted a comeback with the Kansas City Royals last season but was released after allowing 15 hits and five walks in 10 1/3 innings and recording a 7.84 ERA at double-A Northwest Arkansas.

Norris, 34, didn’t pitch last season after injuring his forearm in spring training and getting released by the Blue Jays in April. He agreed to a minor-league contract with the Nationals a few weeks later, but the deal fell through for health reasons. The Phillies signed him after attending his workout for teams last week at Rice University in Houston.

A starter early in his career, Norris began a second act as a reliever in 2016. He recorded 28 saves and a 3.59 ERA for the St. Louis Cardinals in 2018.

Storen can make as much as $750,000 in the majors, according to a source; terms of Norris’ contract are not known.

The Phillies have been mostly quiet since they agreed to a five-year, $118 million contract with right-hander Zack Wheeler on Dec. 4 and a one-year, $14 million deal with shortstop Didi Gregorius on Dec. 11. They have added several veterans on minor-league deals, including infielders Ronald Torreyes and Josh Harrison and outfielders Mikie Mahtook and Matt Szczur, a Villanova product.

Storen and Norris represent low-risk moves for the Phillies, who are stocking up on bullpen arms in lieu of signing established relievers to big contracts as they did with Tommy Hunter, Pat Neshek, and David Robertson in the last two years.

The Phillies are bringing 35 pitchers to camp, including 10 non-roster invitees. And there will likely be more to come before pitchers and catchers report on Feb. 11, as the game of musical chairs slows and free agents swarm the best opportunities they can find.