Kelley's club option for 2020 was declined by the Rangers on Thursday, making him a free agent, Levi Weaver of The Athletic reports.
Kelly (groin) allowed three runs on three hits and one walk while striking out one over one inning in Friday's 14-7 loss to the Yankees.
Kelley left Tuesday's game against the Red Sox with right groin tightness.
The Rangers activated Kelley (biceps) from the 10-day injured list ahead of Wednesday's doubleheader with the Indians.
Kelley (biceps) will pitch in a setup role when he returns from the injured list, Levi Weaver of The Athletic reports.
Kelley was placed on the 10-day injured list with right biceps muscle soreness Monday.
The injury Kelley suffered while warming up during the eighth inning of Sunday's game is described as soreness in his right biceps tendon, Alyson Footer of MLB.com reports.
Kelley left Sunday's game against the Astros after suffering an injury on a warmup pitch, Evan Grant of The Dallas Morning News reports.
Kelley (4-2) allowed two hits across two shutout innings Sunday, striking out two batters and earning the win over Texas.
Kelley allowed two runs on three hits while striking out two in Saturday's 7-4 loss to the Twins.