Saunders has been on the disabled list since getting hit by a line drive in his only start, April 4 at Tampa Bay. An MRI showed only a bone bruise.
The Rangers said Saunders had persistent pain after ''he started to ramp it up'' during his session Wednesday. He will try another bullpen session in a few days.
Right-hander Daniel McCutchen, designated for assignment Monday, cleared waivers and was outrighted to Triple-A Round Rock.
Texas also agreed to a minor league contract with Scott Cousins, a left-handed throwing outfielder they will try to convert to a pitcher. He played in 135 games for Miami and the Los Angeles Angels from 2010-13.