Bautista, 28, could be an interesting contender for the bullpen. The 6-foot-5 right-hander went 2-0 with a 3.74 ERA in 33 2/3 innings before he was designated for assignment by the Giants in early August.
He previously has pitched for the Orioles, Royals, Rockies, Tigers and Pirates and has a career record of 11-15 with a 5.88 ERA in 223 1/3 innings over seven seasons.
MLB.com has learned that Bautista's contract includes language that allows him to request his release if he's not placed on the 40-man Major League roster by March 25. If he makes the Major League roster, he'll earn $800,000, with potential incentives up to another $100,000.
Bautista, the second cousin of Pedro Martinez, is a power pitcher with a fastball in the mid-90s, but control has been an issue. He had an excellent .205 batting average against last season with the Giants and 44 strikeouts in 31 games, but walked 27 batters.
He was sent down to Triple-A after walking four in his final three relief appearances and then giving up a pair of home runs in the sixth inning of a 6-1 loss to Colorado on Aug. 4.
Gimenez, 27, split last year between Cleveland and the Indians' Triple-A club in Buffalo. He hit .190 in 58 at-bats with Cleveland, starting 19 games at catcher and playing in two games in the outfield. He hit .276 with nine home runs and 32 RBIs in 55 games in Buffalo.
Ring, 29, pitched five games with the Yankees last season and has previously spent Major League time with the Mets, Padres and Braves. Over parts of five big league seasons, he's 3-3 with a 5.29 ERA in 99 appearances.
The Mariners have now extended invitations to 13 non-roster players for their Major League Spring Training, which begins with pitchers and catchers reporting Feb. 13 in Peoria, Ariz.