According to Politico, one unnamed source with a "enviable prediction record" this election cycle gives the Wisconsin lawmaker a 54 percent chance of becoming the party's standard bearer.
The GOP source argues he came to the figure after predicting a 60 percent chance of a convention deadlock in July — and a 90 percent chance that delegates then turn to Ryan.
"He's the most conservative, least establishment member of the establishment," the Republican source tells Politico. "That's what you need to be."
Koch has told friends if Donald Trump comes up at least 100 delegate votes short of the 1,237 minimum to secure the nomination, Ryan would be a solid choice.
A source told the Post the Koch brothers support the agenda Ryan is chasing as House speaker, a position he took over last October after John Boehner retired.
The general counsel for Koch Industries, however, told the Post the report was "completely false."
"Let me be clear, we never have advocated for a specific candidate in a presidential primary, and we have no plans to do so now," Mark Holden said.
Politico reports Ryan is "more calculating and ambitious than he lets on," and "is running the same playbook he did to become speaker: saying he doesn't want it, that it won't happen."
An unnamed Ryan friend tells Politico Ryan's speech last month about raising the tone and tenor of politics hinted as much.
"That was somebody who was laying out the speech that, in most cases, you'd give six months before you announce you're going to run — when you're going around the country, raising money for your leadership PAC," the source tells Politico.
"People put my name in this thing, I said, 'Get my name out of that,'" he tells Hugh Hewitt on his radio program Monday, Politico reports.
"This is — if you want to be president, you should go run for president. And that is the way I see it."
Meanwhile, Fox News political commentator Juan Williams declares "Ryan and [Donald] Trump are on a collision course."
In a commentary for The Hill Monday, Williams argues if contender Sen. Ted Cruz can beat the front-runner in Wisconsin on Tuesday, odds "go way up" that Trump cannot win the 1,237 delegates needed to claim the Republican nomination, leading to an open convention that would choose the nominee.
And the man who will preside over negotiations at an open convention is Ryan's friend and fellow Wisconsinite, Republican National Committee Chairman Reince Priebus, Williams writes.
"The real game here is a long-term effort to get the nomination into the hands of a mainstream Republican," Williams writes. "Party elders want someone who will not damage the party's candidates running for the Senate and the House, as well as for state offices."