Murdoch told Fortune that his top choices are "between four or five people."
"It's not necessarily, although slightly, in order of preference: Jeb Bush, Paul Ryan, whom I have particular admiration for. I do for both. [Chris] Christie could recover," he said. "Scott Walker, whom I don't know, and Rand Paul, whom I agree with on a great number of things but disagree strongly on some things -- too strongly perhaps to vote for him."
Murdoch said he disagrees with Paul most strongly on foreign policy. He then detailed what he likes so much about Bush and Ryan.
Why do you admire Paul Ryan?
He is the straightest arrow I've ever met. He's hardworking. He knows where every dollar goes in Washington. He's emerging as the natural leader. I almost think that because of the position he's in, he's not the most important, but he's the most influential Republican in his party at the moment in Washington.
What do you like about Jeb Bush?
I think he's a man of very fine character. He was a great governor. And I particularly like his policy on education, which I'm hardest on. My number one.
His kind words for Ryan come as no surprise. After the Wisconsin congressman was tapped to be Mitt Romney's running mate in 2012, Murdoch hailed it as an "almost perfect choice."
But how would the conservative mogul react to a Hillary Clinton presidency?
"I could live with Hillary as President," he told Fortune. "We have to live with who we get. We don't have any choice."
Asked if he could ever support the former secretary of state, Murdoch said it "would depend on the Republican candidate totally."