In an interview with BBC News 24's My Politics, to be broadcast today, he said that after nearly seven years the prime minister was "too fixed" - a reference to the "no reverse gear" stance he has adopted on Iraq and public service reform.
Lord Healey said: "I hope that Tony will decide to retire from that job in the next year or so because I think that Gordon would do it very well.
"He hasn't got the charisma of Tony Blair but he does at least now start smiling, ever since he married Sarah, and particularly since they had a child ... if you stay in the same job too long I think you tend to get too fixed in your manner of dealing with problems and it's time for a change in that sense and I think that Gordon would do it very well."
Downing Street poured cold water on the idea the prime minister was perturbed by the comments. Mr Blair was preoccupied by his speech on Iraq in his constituency rather than the thoughts of "former government members", his official spokesman said.
He stressed that Lord Healey had suggested Mr Blair should be replaced if no weapons of mass destruction were found or if it were proved he had lied about this. "This is not the first time that Denis Healey has proffered this advice."
Lord Healey, who is not on the left of the party, was the first person to come out the day John Smith died and declare that his successor must be Mr Blair.
Downing Street officials were also in conversation with Number 11 yesterday over the Guardian's story that the chancellor was being lined up in Washington as a possible new head for the International Monetary Fund.
While few in Westminster believed the chancellor would countenance taking the job - with the chance of his becoming prime minister appearing greater amid speculation that a recent deal had been struck - the Treasury did little to scotch the rumours. "This is speculation and it's far too premature to comment," a spokesman said.
Number 10 also dismissed the report as "speculation" and laughed off the idea that the prime minister would back an application.
"I think the prime minister believes the fact that senior members of his government are linked to jobs outside is probably an inevitable fact of political life," said the official spokesman.
"Obviously the IMF is a big job, but the chancellor has got a big job here in the UK."
Friends of the chancellor were at pains to stress that he was less bothered by his job title than "the difference he can make", but the Treasury's failure to quash the story was seen as evidence of his understandable impatience.
The chancellor has always been seen as the prime minister's natural successor, although his "Real Labour" speech at the October conference was widely felt to have damaged him. Mr Blair's confidence in him taking over was also unsettled by that speech.
The IMF's chief economist from 1991 to 2001, Michael Mussa, encapsulated Washington's - and Westminster's - take on the issue.
"Gordon Brown would be an outstanding candidate, but has his eyes and mind and heart set on becoming Britain's prime minister," he said.
