As voters went to the polls in South Dakota and Montana, where a total of 31 delegates are at stake and where Obama is expected to win, AP also reported that Clinton, the New York senator, was to acknowledge after the primaries that Obama had won enough delegates for the nomination.
US media later reported that Clinton had said in a conference call with other New York politicians that she was open to a vice-presidential nomination with Obama, one of the call's participants told the news agency, if it was felt it would help the Democrats in the November presidential election.
But Maria Cardona, Clinton's national campaign spokeswoman, told Al Jazeera both claims were untrue, and said the New York senator felt she owed it to her supporters "to fight until the very end".
"She is not going to concede tonight ... Obama does not have the numbers and until someone has that magic number she is going to continue to press her case," she said.
And John Nichols, a writer for the political journal The Nation, also told Al Jazeera that Clinton and Obama have been in contact for weeks and that, while Obama may not want Clinton as a vice-presidential candidate, there may be discussions on a possible cabinet position for Clinton in any prospective Obama government.
"Obama needs her supporters and her enthusiasm," Nichols said.
The news came as Jimmy Carter, the former US president and a senior Democrat "superdelegate", said on Tuesday that he would endorse Obama, a huge boost for first term senator.
About 180 superdelegates - senior party officials who can choose to back either candidate at August's convention in the state of Colorado - are still to declare their support.
However, many analysts feel that their endorsements could start to stream in once the state nominating contests are over, possibly clinching the contest for Obama.
On Tuesday, Obama also gained the endorsement of US representative James Clyburn, the highest ranking African-American in the US congress.
|A Clinton adviser told Al Jazeera she would |
fight on "until the very end" [EPA]
Rob Reynolds, Al Jazeera's Washington correspondent, said earlier on Tuesday that it does appear that, bit by bit, Obama is closing in on the Democrat nomination and by Tuesday evening, if he has enough superdelegates, he could well stand before a crowd in Minnesota, where he is campaigning, and say he has won the nomination.
Clinton is due to head back to her senate seat of New York for an event on Tuesday evening, prompting speculation that she was planning to end her campaign.
Bill Clinton, her husband and former US president, also sounded as though the campaign was winding down when he spoke to voters in South Dakota.
"This may be the last day I'm ever involved in a campaign of this kind," he said.
But the former first lady said that Tuesday marked "the beginning of a new phase of the campaign".