04/22/2012 07:05 pm ET Updated Apr 22, 2012

Marco Rubio: Jeb Bush Would 'Be A Fantastic Vice President'

As he continued to deny any interest in becoming Mitt Romney's running mate, Sen. Marco Rubio instead turned the veepstakes spotlight on fellow Florida Republican Jeb Bush, who he said would make a "fantastic vice president."

During an appearance on CNN's "State of the Union" on Sunday, the freshman senator said he believed the former governor should accept the place on the ticket if offered it by likely GOP presidential nominee Mitt Romney.

"I hope he'll say yes if future President Romney asks him," Rubio said. "I think he'd be a fantastic vice president."

Rubio continued: "But let me just say this about the vice presidential process. Up to now it's all been theoretical; we have a nominee now, and our nominee, Mitt Romney, the leader of the Republican Party, has a vice presidential process in place. And I think from this point moving forward, I think it'd be wise for all Republicans to kind of respect that process, myself included, and say moving forward, we're going to let his process play itself out."

His comments came just days after Bush, a popular figure in the Republican Party who many had hoped would seek the presidential nomination, said that Rubio should be Romney's running mate.

"Well I can’t speak for Gov. Romney, and I can’t speak for Sen. Rubio, but if I was on both sides of that conversation I would ask -- and I would hope that Marco would accept,” Bush said in an interview with Newsmax.

"There’s a lot of things in between that may not make that happen," Bush said. "But I am a great admirer of Mitt Romney’s and I’m a huge fan of Marco Rubio’s, and I think the combination would be extraordinary.”"

While both Bush and Rubio have endorsed Romney, they have also both insisted that they are not interested in seeking the vice presidency.