Tony Blair will leave Downing Street "well before" the next general election, Jack Straw has predicted.
Straw says he would like to be the next deputy prime minister
The Commons leader, who was foreign secretary until May's reshuffle, said he would like to take over from John Prescott when he quits as deputy PM.
Mr Blair has continually side-stepped questions about his departure, saying that the speculation "gets in the way".
He has said he will serve a full third term but allow for a "stable and orderly transition" to his successor.
'Fuelling a fire?'
But Mr Straw, in an interview with The Spectator magazine, said: "Everybody knows that Tony will go - go well before the next election - that unless something astonishing happens, that I'm not anticipating, that Gordon is his successor."
He also confirmed he had authorised briefings over the weekend that he intended to apply for the deputy leadership of the Labour Party when Mr Prescott eventually goes.
"Look, what's been said on my behalf has been said, and everyone faces a dilemma between dissembling and fuelling a fire," he said.
"People have been reasonably candid on my behalf. It was precisely because I didn't want to dissemble that the message was put out on my behalf on Friday and Saturday."
Northern Ireland Secretary Peter Hain, Education Secretary Alan Johnson and Constitutional Affairs Minister Harriet Harman have also been named as potential contenders for the post of deputy prime minister.
Elections 'are debilitating'
Mr Straw said he would be "astonished" if Mr Brown was not elected unopposed by the party as Mr Blair's successor when he quits.
"I think there'll be one candidate. And I think that'll be a great relief to people because, if there is one obvious candidate, why on earth spend so much time and money, let me say, in the party having an unnecessary contest?" he said.
"You could argue that elections can be cleansing. I have to say that this was a very sedulous argument that was put forward during the dog days of Labour opposition, that elections were cleansing.
"On the whole they were absolutely bloody debilitating."
Mr Straw, 59, also revealed he had suffered from a "horrible" bout of pneumonia in February, which forced him to take a week off work.
He also told the magazine he was "sceptical" and at the "cautious end of the spectrum" on the state funding of political parties - one of several controversial issues in his in-tray.
And he spoke of his regret that he and then US Secretary of State Colin Powell did not win the argument with the Pentagon over who would take charge of post-war reconstruction in Iraq.
He tells Spectator editor Matthew D'Ancona of his attempt in February 2003 to persuade sceptical members of the UN Security Council of the merits of military action.
Mr Straw had argued the Americans' record in Germany and the Japan after the Second World War showed they were "good nation-builders".
In a separate development, Mr Straw this week resumed the tradition - abandoned by his predecessor Geoff Hoon - of the Commons leader giving a weekly briefing to lobby journalists.