Lee felt some discomfort in the area of his back where he recently got a cortisone shot, and he didn't go through with his scheduled bullpen session before Saturday's game at Minnesota. He threw in the outfield instead.
Lee will try to throw off a mound before Sunday's game, and then a decision will be made about whether he'll start Tuesday at Toronto.
"I feel better today than yesterday," Lee said. "If I see the same improvement tomorrow, we're definitely heading in the right direction."
The Rangers also took out shortstop Elvis Andrus in the fourth inning on Saturday, replacing him with Cristian Guzman because of tightness in his hamstrings. Trailing 9-1, the Rangers also removed center fielder Josh Hamilton and catcher Bengie Molina.
Hamilton, who left Friday's game early because of tightness in his lower back and also missed two games earlier this week following a painkilling shot in his knee, bruised his ribs after a running catch into the wall.
Manager Ron Washington said Hamilton would probably be out for the next two days. Precautionary X-rays were negative. Hamilton said the injury is similar to the one he endured last season that put him on the disabled list.
Andrus is day to day. He's been playing with the injury for "a while," Washington said.