"I'd like the remaining 350 super-delegates to say who they're on between now and July 1," he said. "There has been some personal criticism. We don't want this to degenerate into a big fight at the convention," The Telegraph quoted Dean, as saying.
Senior party leaders such as Dean, Nancy Pelosi, former vice-president Al Gore and Harry Reid, the Senate Majority leader, could decide to take a public stand if they believed Hillary was continuing to fight on beyond the point where victory was possible.
Mark Mellman, a Democratic pollster who is also remaining neutral, said that a bitter fight at the convention would make it difficult for the defeated candidate's supporters to rally behind the nominee.
"There is no way that Hillary is going to win enough delegates to get the nomination," said Patrick Leahy, a Vermont senator.
"She ought to withdraw and she ought to be backing Senator Obama," he added.
Hillary's options appear to be narrowing by the day. Her aides concede that she cannot overcome Obama's lead among pledged delegates, which currently stands at 166, and will struggle to erase his 700,000 advantages in the popular vote.
Her remaining hope lies in persuading a large number of the "super-delegates" - 796 members of Congress and other party officials - that she would be a better candidate than Obama against John McCain, the Republican nominee.
This would mean the super-delegates overturning the will of the Democratic voters, effectively mounting a party coup d'etat against a man within striking distance of becoming America's first black President.