Percival, 39, went on the disabled list Friday for the third time this season after suffering a cartilage injury in his right knee during the ninth inning of Thursday's 7-6 win over the Athletics.
Percival said he has been on anti-inflammatory medication since Friday, and his knee feels much better.
"I felt good today," Percival said. "I played catch [and] had pain, but nothing debilitating."
Percival was supposed to be seen again by Keith Meister, the Rangers' orthopedic doctor, on Sunday, with a decision expected either Sunday night or Monday morning regarding whether he would have arthroscopic surgery or proceed without surgery.
The prognosis for Percival's recovery is two to four weeks. If he avoids surgery, it's likely the recovery period would be quicker.
Percival said he was encouraged after playing catch Sunday.
"Made about 30 throws," Percival said. "I couldn't have pitched today, but if I made the same progress tomorrow I would have been able to pitch."
Percival is 2-0 with 27 saves and a 3.69 ERA this year. He has held opponents to a .162 average, which ranks sixth lowest among Major League relievers. His 351 career saves rank seventh on the all-time list. The Rays are 32-0 in games when he enters in a save situation.
Bill Chastain is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.