"Tommy's doing very well," manager Mike Scioscia said. "He's going to throw another bullpen and then hopefully he'll have a rehab start next weekend and see when he's ready to be put back in our rotation.
"He threw about 38 pitches and his stuff looked very good."
Will he be ready by the 23rd?
"We're not going to try to fit a square peg into a round hole," he added. "If he progresses and is ready, I would hope he'd be a candidate, but he needs to go out and pitch and we'll evaluate where he is."
Scioscia added that the rotation is set for the first four games of the second half, although he was not ready to reveal it yet.
Three other injured pitchers are not quite as far along: right-hander Ryan Madson (right elbow), left-hander Sean Burnett (left elbow impingement) and left-hander Jason Vargas (blood clot).
Bob Sherwin is a contributor to MLB.com.
This story was not subject to the approval of Major League Baseball or its clubs.