The actor also must acknowledge that "his work reflects anti-Semitism," particularly the 2004 hit movie "The Passion of the Christ," Reiner told Associated Press Radio.
"When he comes to the understanding that he has done that, and can come out and say, you know, 'My views have been reflected in my work and I feel bad that I've done that,' then that will be the beginning of some reconciliation for him," Reiner said.
Some critics attacked Gibson's movie as portraying Jews as evil. Supporters said the movie was merely being faithful to Gospel accounts of Jesus's arrest and crucifixion.
A call to Gibson's publicist seeking comment was not immediately returned Friday.
Gibson publicly apologized for an anti-Semitic tirade he unleashed when he was arrested for drunken driving in Malibu on July 28. He has called the remarks "despicable."
Earlier this month, Gibson pleaded no contest to a misdemeanor charge in a deal that calls for alcohol rehabilitation, fines and probation.
Reiner, however, said Gibson also must do some "major soul-searching."
"It's not a matter of just apologizing for some words you've said," Reiner told Associated Press Radio. "It's to really understand why it is you're anti-Semitic and where those feelings came from."
"I believe that people can be redeemed and people can change, but that's going to be a very long process," he added.