"I would like to," Murdoch said. "I'm a great admirer of hers. And I've had long talks with her."
Representatives from Fox and DreamWorks did not immediately respond to requests for comment, but Snider's status has been the subject of intense speculation this spring. Insiders tell TheWrap that her current contract at DreamWorks runs through the end of 2014, but as Murdoch indicated the interest in her is heating up.
If she were to join Fox, she would provide creative oversight and playing traffic cop to Fox's various production divisions, a group that includes Fox 2000, Fox Searchlight and Fox Animation, according to several individuals. It's a role similar to the one that former Warner Bros. Motion Picture Group President Jeff Robinov considered taking before talks broke down last year. She would report to studio chief Jim Gianopulos.
To leave her contract, Snider will need the approval of DreamWorks principal partner Steven Spielberg, one individual with knowledge said.
The Snider talks weren't the only pearl to come out of an unusually candid sit-down with Fortune. Murdoch guards his private life zealously, but hinted that he was wounded by a recent Vanity Fair report that his ex-wife Wendi Deng wrote long diary entries chronicling her erotic feelings for prominent figures and family friends such as former U.K. Prime Minister Tony Blair.
"I was shocked," Murdoch said. "But I didn't read them and I was not given them until after I had filed for divorce."
A representative for Deng did not immediately respond to a request for comment.
But it wasn't all regrets and recriminations. Murdoch indicated that he's a resilient fellow.
"Well, [people] perhaps tend to think I've not got as thick a skin as I have," he told Fortune. "You know, I don't mind what people say about me. I've never read a book about myself."
When it comes to the presidential election, Murdoch said he is rooting for former Florida Gov. Jeb Bush to become the Republican front-runner, but also said he respects Rep. Paul Ryan, Wisconsin Gov. Scott Walker, Sen. Rand Paul and New Jersey Gov. Chris Christie.
" I think [Jeb Bush is] a man of very fine character," Murdoch said. "He was a great governor. And I particularly like his policy on education, which I'm hardest on. My number one."