Gov. Bob McDonnell, the new chairman of the Republican Governors Association who has been mentioned as a possible vice presidential candidate, said Monday that he may not endorse in the presidential race.

But, he said in an interview with The Washington Post, he will make a final decision after November following Virginia’s legislative elections.

“It’s still very early in this cycle,’’ he said. “I’ll evaluate the situation in November and December as far as my endorsement and whether or not being the RGA chairman...about whether it’s proper for me to get involved with an endorsement at all.”

McDonnell was named RGAchairman on Monday, after Texas Gov. Rick Perry, who had been serving as chairman, entered the presidential race. He had little to say about the race, except that he thinks a governor would make the best president, but he has met with a number of candidates. He supported former senator Fred Thompson in 2008.

It would make sense for McDonnell to sit out the race if he has an eye on the the vice presidential spot .

“I’m not campaigning for it. I’m not lobbying for it. I’m not asking for it. I’m not expecting it all,’’ McDonnell said. “All I’ve said is if any governor in America gets a call from a candidate and says ‘Hey, I’d like you to help my ticket. Would you be on it?’ I’d say sure, I’d think about it.”

McDonnell said he intends to complete his term as governor, which ends in January 2014. But that didn’t stop Virginia Democrats from pouncing on his statement.

“Bob McDonnell’s announcement that he wants to leave office to become vice president sheds a lot of light on his empty rhetoric on jobs, his gimmick-laden budgets and his borrow-and-spend transportation plan,’’ said Brian Coy, a spokesman for the Democratic Party of Viginia. “As Virginians cope with the loss of 14,000 jobs in the month of June, it’s clear that he’s hoping Michele Bachmann or Rick Perry will whisk him away before the bill comes due for his failed agenda.”

McDonnell was one of many who criticized former governor Tim Kaine for serving as DNC chairman his final year as governor because they said he spent too much time away from Virginia.

“The problem with the DNC chair is [that it’s] a full-time job,’’ he said. “It’s a full-time, paid job that governor Kaine was trying to do part time while he was part-time governor, and that was my criticism. I think this is very different.”