The choice was first reported online by TheWrap, the Reporter said.
Kerrey is a Medal of Honor winner from his U.S. Navy service in Vietnam, where he lost a leg in combat.
He has not officially accepted or negotiated a deal, but the Reporter said the MPAA job is his if he wants it.
If he accepts, Kerry would replace Bob Pisano, interim president since Dan Glickman left in March. Pisano recently denied he was interested in continuing in the position, the Reporter said.
An MPAA spokesman declined comment on the report.
Kerrey was in the U.S. Senate from 1989 until 2001, after serving as Nebraska governor, and was an unsuccessful candidate for president in 1992. Since leaving the U.S. Senate, he has been president of The New School, a New York City university.