Sunday is Padilla's third rehab start after he allowed one run in 4 2/3 innings for Class A Inland Empire on Tuesday. Sunday would be Padilla's first rehab start above Class A.
Padilla is scheduled to spend Sunday night in Oklahoma City then join the Dodgers on Monday in Cincinnati.
"We'll see what it looks like when he comes in there and how he felt," manager Joe Torre said. "We expressed, or at least I expressed to him to be sure we're 100 percent ready to go."
Padilla has been on the disabled list since April 23 with a nerve injury in his pitching arm.
After Monday's off-day, the Dodgers rotation will likely kick off with Hiroki Kuroda on Tuesday, then Clayton Kershaw on Wednesday, Torre said.