Bush said he has been a huge fan of Rubio's for years and hopes that Romney chooses him. He said he made his pitch to Romney in a recent conversation, but the former Massachusetts governor didn't reveal which direction he was leaning. Bush said the choice is a personal one and respects Romney for keeping his thoughts close to his vest.
Romney has said he is considering Rubio, a freshman senator who was elected in 2010.
In an interview with The Associated Press, Bush also criticized President Barack Obama, saying he believes he has deliberately chosen to divide rather than lead as a campaign tactic.
"Finding solutions isn't the ultimate goal and this has been exacerbated by President Obama's unwillingess to lead on the big structural problems we face and he does it because I think he believes it's easier to win a close election by dividing rather than trying to find solutions," Bush said. "I think the next president should be focused on problem solving rather than making political points."
Separately, the nonpartisan Commission on Presidential Debates said Wednesday that the third and final debate this fall will take place Oct. 22 at Lynn University in Boca Raton. It will focus on foreign policy.
Bush criticized the lack of action on making changes to entitlement programs to address their rising costs, saying no proposals have been offered. And he used illegal immigration as an example of an issue that has gone unaddressed for political purposes.
When Democrats controlled the House and Senate during Obama's first two years in office, Obama could have more easily passed a plan to address illegal immigration than pass the health care overhaul, yet he did nothing, Bush said.
"They want to keep it alive so it keeps coming back," Bush said.
Bush, who left office in 2007 and remains influential in Florida politics, said he has done about six political events for Romney and has several more planned. He also has helped congressional candidates in California and New York, as well as Virginia Senate candidate George Allen.
But as far as his own political future, Bush said he has no thoughts of running for any office in the future, staying content discussing policy issues as a non-candidate.
And while the Republican National Convention will be in Tampa, he said he hasn't been invited to speak.
"I haven't even given it any thought to be honest with you. I'm not expecting to speak," Bush said, noting he did not speak at the GOP conventions when his brother, George W. Bush, was president or at all when he was governor. "I was a bigger dog back then, probably."