CNN — Former Gov. Jeb Bush of Florida is not being vetted for the job of vice president by presumptive Republican presidential nominee Mitt Romney, his son said in a Monday interview.

"He's not being vetted right now," George P. Bush said on CNN's "The Situation Room with Wolf Blitzer." "He's one of the few politicians that does what he says in the sense that he's not actively pursuing a higher office."

The former Florida governor has been suggested by some as a potential number two for Romney's ticket, although he said as recently as last month that "under no circumstances" would he run.

George P. Bush, who is the nephew of former President George W. Bush and grandson of former President George H. W. Bush, said that his father has a level of influence without a spot on the ticket and will "do whatever he can" in aid of electing Romney.

"I think he has a voice within the Republican Party as a conservative, especially as it relates to education reform," George P. Bush told CNN's Wolf Blitzer.

"I see him working hard on behalf of Governor Romney in some key battleground states, but like me he's going to do whatever he can when he's called to service this fall on behalf of the governor."

Jeb Bush said in a June interview that this year may have been his "window of opportunity" to run for the White House himself, but has not ruled out the possibility of a future run.

George P. Bush also said his father and Sen. Marco Rubio of Florida would be useful surrogates and "provide a very diverse message on behalf of the Republican Party in a key battleground state like Florida."

His father drew attention last month for telling reporters that Ronald Reagan and his own father, former President George H. W. Bush, "would have a hard time if you define the Republican Party -- and I don't -- as having an orthodoxy that doesn't allow for disagreement, doesn't allow for finding some common ground."

Jeb Bush took to Twitter in his own defense, posting, "The point I was making yesterday is this: The political system today is hyperpartisan. Both sides are at fault."

George P. Bush said his father was advocating for the GOP to be more of a "big tent" which welcomes people of different backgrounds, including Hispanics and supporters of the tea party.

"I think what my dad was trying to say was we need to be the party that is more welcoming, that allows people from various backgrounds to come in whether they have labels behind their name or not," he said.

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-- CNN's Ashley Killough and Gregory Wallace contributed to this report

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