The Times ran an interview with Deputy Prime Minister John Prescott on its front page under the headline "Race to seize Blair's crown is under way".
Prescott's office issued a statement on Saturday saying the Times headline was "untrue".
In the interview, Prescott was quoted as saying senior ministers had discussed a future without Blair and suggested they were preparing for a seismic shift in government.
"I think it is true that, when plates appear to be moving, everyone positions themselves for it," Prescott said in the interview with the Times.
Asked if senior ministers were preparing for a new leader or had discussed it, Prescott said: "Yes, people do talk about it and you get that discussion ... every British prime minister goes eventually."
But in the statement issued on Saturday Prescott played down the significance of his comments. "Of course there has been speculation over the leadership, but the reality is there is no race for the prime minister's position," he said.
Blair's office declined to comment. His spokesmen have repeatedly denied rumours he is planning to resign before an election expected next year.
War and popularity
Blair's trust ratings plummeted after the Iraq war and his government has been hit by negative headlines on issues from Europe and the Middle East to health and public services.
John Prescott (L) has denied
reported statements about Blair
Blair, who swept to power with a landslide election win in 1997, dismissed talk of his resignation as "froth" on Friday. But newspapers have speculated there is growing support within the government for Chancellor of the Exchequer Gordon Brown, Blair's key ally and main rival for the leadership.
Prescott confirmed in the Times interview Blair and Brown had a "pretty serious breakdown in relations" soon after Labour came to power, but said they had been working "extremely well" together more recently.
Political folklore says the pair have made a pact in 1994 that if Blair became prime minister he would one day step aside to allow Brown to take over.
Prescott admitted Labour had been "rather dampened by the whole business of Iraq".
"We understand that it has been difficult," he told the paper.
The latest Populus poll put support for Labour at 32%, four points behind the Conservative Party and a 17-year low.