Manager Don Mattingly wouldn't rule out the possibility, despite already announcing that Aaron Harang would take Kershaw's place on short rest.
"It's all about the timetable," Mattingly said. "We'll see how he bounces back tomorrow."
Mattingly said Kershaw threw well enough, and without any visible signs of pain, that the manager would be comfortable enough to start him Sunday if medical clearance is given.
"He's been throwing the whole time," Mattingly said. "The doctors, the medical staff -- if he's pain free, he can pitch because he's not hurting himself. But he's got to be pain free.
"It has to be the medical people saying he's passed every test and cleared every hurdle. It's an organizational decision, not my decision. Does it make sense? A guy with his upside, they're not going to leave that decision only in my hands."
Kershaw said he felt good and was able to throw all of his pitches. He said as long as the Dodgers are alive for a postseason berth, he's determined to pitch.
The session was watched by medical director Stan Conte and pitching coach Rick Honeycutt "to make sure mechanically he does what he always does," said Mattingly. "He did some running. We'll see what happens tomorrow."
Since Sept. 4, Kershaw has started one game on Sept. 11, three days after receiving a cortisone shot in the hip. He allowed one unearned run on three hits over seven innings against Arizona, but hasn't pitched in a game since.
"It's taken until now to be pain free," Mattingly said.
In the aftermath, his hip was inflamed enough that he scrubbed a scheduled bullpen session last week and was scratched from a Sunday start.
Kershaw would not discuss details of his injury or confirm whether he needs surgery to repair a torn labrum, as has been widely speculated.
Such an arthroscopic operation -- similar to one performed on teammate Jerry Hairston last week -- would take three to five months for recovery. In addition to repairing damaged labrum, the surgery usually involves shaving down an irregularity in the neck of the femur.
Kershaw and Mattingly ruled out the possibility that he would be used in relief.
Ken Gurnick is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.