Donald Trump. AP Photo/Julie Jacobson

Donald Trump on Monday dropped his biggest hint yet as to whom he'd consider as a potential vice president.

The Republican frontrunner name-dropped former presidential candidates Marco Rubio and Scott Walker along with John Kasich, one of the three remaining men vying for the GOP nomination.

"There are people I have in mind in terms of vice president," he told USA Today. "I just haven't told anybody names ... I do like Marco. I do like Kasich … I like Walker actually in a lot of ways. I hit him very hard ... But I've always liked him. There are people I like, but I don't think they like me because I have hit them hard."

Trump previously suggested he wanted someone with experience in government, as opposed to an outsider like him.

Both governors, Walker of Wisconsin and Kasich of Ohio, quickly responded to the news.

Walker told the Wisconsin State Journal on Monday that he was "shocked" the GOP frontrunner was considering him as a running mate. Walker endorsed Ted Cruz, Trump's top competitor in the primary.

Though Walker said he laughed after reading Trump's remarks, he wouldn't rule out accepting the job.

"It's kind of interesting to hear that after the things that were said about me a couple weeks ago," he said. "It's almost breathtaking that I was listed in the first place."

But he added that the Republican nominee might not be even able to choose his running mate, given the likelihood of a contested convention in which the delegates could fill out the ticket.

Kasich was much more blunt in his response to the news. He told CNN's Anderson Cooper on Monday that there was "zero" chance he would serve as Trump's vice president.

"I'm not going to be anybody's vice president," the Ohio governor said. "I'd be the worst vice president the country ever saw. You know why? Because I'm not like a vice president. I'm a president. You know?"