The A’s never shy away from bringing back their former players and they’re set for another reunion soon.

According to multiple sources, Oakland is close to adding left-hander Jerry Blevins on a minor-league deal. The reliever, who spent the past four years with the Mets and 2014 with the Nationals, was a part of the A’s 2012-13 playoff teams.

According to a source, the big-league portion of Blevins’ deal is worth $1.5 million. He will be a non-roster invitee to spring training.

Blevins, 35, was particularly instrumental during the stretch run in 2012, with a magnificent performance at Anaheim on Sept. 11. After closer Grant Balfour allowed two runs in the ninth, Blevins took over with the potential tying run at third and potential winning run at first, struck out Kendrys Morales and got Howie Kendrick to hit into a game-ending double play.

In 267 innings with Oakland, Blevins put up a 3.30 ERA; he had a 3.38 ERA in his four years in New York, including 4.85 last season.

The A’s have only one left-handed reliever, Ryan Buchter, on their 40-man roster, so Blevins will have decent shot at making the big-league roster. There are two other lefty relievers among the non-roster invites, Kyle Crockett and Dean Kiekhefer and left-handed swingman Kyle Lobstein also will be competing for spots.

Susan Slusser is a San Francisco Chronicle staff writer. Email: sslusser@sfchronicle.com Twitter: @susanslusser