The former Florida governor and longtime supporter of Rubio told the Associated Press that he personally lobbied on Rubio's behalf in a recent conversation with Romney. Bush said Romney did not indicate who he would choose.
Rubio, a freshman senator who was elected in 2010, is a rising star in the Republican Party. He is also a favorite of the tea party movement.
Romney said last month that Rubio "is being thoroughly vetted" as a possible vice presidential choice.
Rubio has said repeatedly that he does not expect to make the ticket.
"I'm not going to be the vice president," he told the Tampa Bay Times in March.
His position shifted a bit as it became clear that Romney was considering the Florida senator.
Rubio refused to comment on the topic last month, telling Fox News that he wanted "to be respectful" of Romney's process for selecting a running mate.
Bush, whose brother and father were president, recently lamented not running for president himself.
"This was probably my time," he told "CBS This Morning" in June.
Bush said he was not interested in being Romney's vice president -- "I'm not going to do it" -- but said he could still have some influence from the sidelines.
"That doesn't mean I don't have a voice," Bush said. "It doesn't mean I don't want to enthusiastically support Mitt Romney. I intend to do that, I'm doing it. He's got a great list of candidates that I'm sure he's thinking about."
Bush told the Associated Press that he does not expect to speak at the Republican National Convention in Tampa, Fla., noting that he didn't speak even when his brother, George W. Bush, was the party's nominee.
"I was a bigger dog, back then, probably," he said.
Romney told NBC's Brian Williams on Wednesday that he has not yet chosen his running mate, and that he won't announce a decision while he's overseas.
"But when the decision is made, I'll make that announcement," he said. "It’s not made yet."
Romney is on a six-day trip that began in London and will include stops in Israel and Poland.