WH: Potential Clinton-Biden contest 'not weighing on the President's mind'

Washington (CNN) -  What happens if the co-captains of President Barack Obama's "Team of Rivals" run for president?

A potential match-up between Vice President Joe Biden and former Secretary of State Hillary Clinton, that once seemed far-fetched, is increasingly sounding more plausible.

[twitter-follow screen_name='politicalticker'][twitter-follow screen_name='JimAcostaCNN']

Biden is making it clear in nearly every interview he grants that a run for the Democratic presidential nomination in 2016 is something he is considering, even if it means taking on the former secretary of state.

Both Clinton and Biden have delivered speeches this week that have sounded more like campaign pitches and less like addresses on their usual portfolios of issues.

Asked about the prospect of a race between the two close allies of the president, White House Press Secretary Jay Carney said the question was so "far off" that he would not even "entertain" it.

"The questions about an election that is very far in the future are not weighing on the president's mind right now," Carney said.

But pressed again by reporters, Carney described both Biden and Clinton as valuable to the president.

"What I can tell you is, the president is very appreciative of the service that Secretary Clinton gave to this administration and to the President's foreign policy team, and she did excellent work. And they have a very good relationship," Carney said.

"And the President continues to be enormously grateful for the excellent partner he has in Vice President Biden and has had since the beginning of this administration," he added.

The Vice President has increasingly sharpened his partisan tone in recent speeches.

Speaking at the Democratic National Committee's Winter meeting, Biden said the party should not apologize for its positions on the issues.

Republicans are "not for much," Biden said, adding "what they're for they don't want to talk about."

In an interview with Politico, the twice failed presidential candidate (Biden ran in 1988 and 2008) sounded as if he's weighing a third run.

"I think I'm qualified by the record I have demonstrated over the years, by the experience I have, by the significant knowledge I have of not only foreign policy but individual leaders in foreign countries and domestically as well."

Carney attributed Biden's comments to the vice president's plain-spoken style.

"You know Vice President Biden. I know Vice President Biden. When he's asked a question, he answers it. That's what he does."

A contest between the vice president and former secretary of state could hone her political skills for the 2016 campaign, one Democratic adviser who supports Clinton said.

"No sensible person thinks that Hillary will be unopposed," the adviser said, acknowledging a possible Biden candidacy.

"Biden-Hillary might be like Obama-Hillary, which strengthened the party and sharpened Obama. Biden is enormously talented – and strong where Hillary is strong: with the middle-class working people you need to win. So if he runs that could be a very good thing," the adviser added.

Not all Democrats are convinced Biden would take on Clinton.

"I really don't think it will happen," another Democratic adviser said.