Reporter Ken Rosenthal says teams can put in a claim on Padilla until 1 p.m. ET Friday. Any team that claims him would assume his remaining salary of approximately $8 million.
Few clubs are in position to absorb such a payroll hit, making it doubtful that Padilla, 31, will be claimed.
Padilla, making his first start since coming off the disabled list with a strained right shoulder, allowed seven runs in 3 2/3 innings in a 12-3 loss to the Yankees on Tuesday night.
Connecting you to your favorite North Texas sports teams as well as sports news around the globe.
He is said to be healthy, and went 2-0 with a 1.57 ERA in his three starts before going on the DL. For the season, however, he is 3-3 with a 5.57 ERA.
If Padilla goes unclaimed, the Rangers can attempt to send him to to the minors.
Padilla would have the right to refuse and would become a free agent.