Speaker Paul Ryan Paul Davis RyanKenosha will be a good bellwether in 2020 At indoor rally, Pence says election runs through Wisconsin Juan Williams: Breaking down the debates MORE (R-Wis.) is refusing to definitively rule out the possibility that he would accept the Republican presidential nomination if the GOP convention is deadlocked.

"You know, I haven't given any thought to this stuff," Ryan told CNBC’s John Harwood in an interview published late Tuesday night. "People say, 'What about the contested convention?' I say, well, there are a lot of people running for president. We'll see. Who knows."

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Ryan emphasized that he made a conscious decision not to run for president, but he left the door open to accepting the nomination as a potential last-ditch solution.

"I actually think you should run for president if you're going to be president, if you want to be president," he said. "I'm not running for president. I made that decision, consciously, not to."

The likelihood of a contested convention increased on Tuesday after Republican presidential candidate John Kasich scored a victory over front-runner Donald Trump Donald John TrumpObama calls on Senate not to fill Ginsburg's vacancy until after election Planned Parenthood: 'The fate of our rights' depends on Ginsburg replacement Progressive group to spend M in ad campaign on Supreme Court vacancy MORE in his home state of Ohio, leaving a tougher path for Trump to clinch the nomination.