"So I don't know how somebody who is in second place is offering the vice-president to the person in first place," he told the rally in the city of Columbus.
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On Saturday, Bill Clinton, the former president, had said that a presidential campaign headed by his wife, with Obama in the number two slot, would be an "almost unstoppable force".
Hillary Clinton said on Monday in Pennsylvania that "a lot of Democrats like us both and have been very hopeful that they wouldn't have to make a choice".
"But obviously Democrats have to make a choice and I'm looking forward to getting the nomination.''
Experience issue
The New York senator has repeatedly questioned Obama's bid by casting doubt on whether he has the experience to become US commander-in-chief.
Obama, an Illinois senator, said it made no sense for Clinton to suggest he was not ready to be president and then hint that she might hand him a job that could make him president if she is incapacitated.
"If I'm not ready, how is it that you think I should be such a great vice-president?'' he said.
Many political analysts have also rejected the idea.
They say the two senators lack a warm relationship and insiders have said Obama could be frustrated in the vice-president's job, especially in a White House where Bill Clinton is very likely to play a big advisory role.
A total of 2,025 delegates are needed to win the party's nomination to stand in the November polls and the 795 Democratic "superdelegates" are set to play a crucial role in deciding the nomination.