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By Steve Holland

WASHINGTON, Nov 7 (Reuters) - President Barack Obama said on Thursday he would have rejected any plan to replace Joe Biden with Hillary Clinton as his vice president for the 2012 election.

In an interview with NBC News, Obama did not deny that his political aides had poll-tested the idea of having him run for re-election with Clinton as his No. 2 instead of Biden.

Obama's top aides considered the idea but decided not to pursue it because it did not materially improve Obama's odds, according to "Double Down," a new book on the 2012 campaign by journalists Mark Halperin and John Heilemann.

"People do all kinds of stuff," Obama said. "Some of it, they clear with me, sometimes they're trying to figure something out, particularly on the political side."

But Obama, who won re-election with Biden at his side a year ago over Republican Mitt Romney, said if aides had asked him whether he wanted to replace Biden, he would have told them, "...there is no way that I'm not running again with Joe Biden."

"I like him. When my back's up against the wall, he has my back," he said.

The saga is significant because both Clinton, a former secretary of state, and Biden are considered to be potential candidates in a race for the Democratic presidential nomination in 2016.

Biden, who would be the underdog should he and Clinton compete against each other, would not want to deal with a narrative in which Obama had considered replacing him.

Some Biden supporters have questioned whether the president was showing sufficient loyalty to his No. 2. Obama's remarks appeared to be aimed at repairing any damage.

Obama said he and Biden had talked about the issue of replacing him in the wake of the book's revelations.

"What I told him, and he knows and he believes me, is that I would not, I would not be here if it weren't for the support I've had from Joe Biden. He is a personal friend and adviser," Obama said. (Reporting by Steve Holland; Editing by Eric Walsh)