Environment Secretary David Miliband will not run for the Labour leadership, once Tony Blair stands down, the BBC understands.
Some Blairite MPs favour Mr Miliband as a potential leader
BBC political editor Nick Robinson said Mr Miliband wanted to end speculation he would run against Gordon Brown.
Mr Miliband told the BBC: "I'm not wavering... I am not a candidate."
Mr Blair is expected to announce his resignation after the 3 May elections and Mr Brown remains the firm favourite to succeed him.
Nick Robinson said Mr Miliband is anxious to kill off rumours he was waiting for the results of the Scottish, Welsh and local elections, before deciding whether to run against the chancellor.
But, our correspondent added, sceptics will accuse Mr Miliband of allowing himself some "wiggle room" by not clearly stating he will not run and would not accept nomination.
Earlier Mr Blair ducked questions about Mr Miliband and the Labour leadership at his monthly press conference.
Asked what his advice for the environment secretary was, he replied: "I don't give advice to anyone in that situation, so ... I've said that I'll say nothing about this, and I mean it.
He added: "If I even raise an eyebrow out of place it is over-interpreted. So, I've got nothing to say on that."
Mr Miliband made his plea in a BBC interview earlier on Tuesday.
Asked whether he thought he should run for the Labour leadership, he said: "Well I've not wavered in my view over the last three years and I'm not wavering now.
"I've meant what I said, I am not a candidate, we've got an excellent prime minister in waiting in Gordon Brown, and I'm getting on with my job as environment secretary which I think is one of the most pressing issues that we face."
Senior Labour MPs, some close to Mr Blair, have heaped praise on Mr Miliband - including John Reid, Charles Clarke and Alan Milburn, in an effort to persuade him to stand.
But one would-be supporter told the BBC some MPs had made it impossible for Mr Miliband to stand for the leadership, by presenting him as a "Blairite" candidate.
"This is simply continuing the Blair v Brown feud," added the MP, who did not want to be named,
According to press reports, Mr Miliband's supporters will nominate him for the leadership - whether he has entered the race or not - in an effort to demonstrate the strength of support for him - and that Mr Brown is "beatable".
They are hoping he will change his mind when he sees the number of nominations he has received, which will be listed on the Labour Party website, it is reported.
He will have until noon on the day after nominations close to decide whether to challenge for the leadership or not.
Only two other potential candidates, both from the left of the party, have announced their intention to stand against Mr Brown - Michael Meacher and John McDonnell.
But there are questions over whether either will get the 45 nominations necessary to get on to the ballot.
Mr McDonnell said on Tuesday: "Now that [it] is confirmed that David Miliband is not willing to be a candidate, it is absolutely clear that the only way that Labour Party members will get a say in determining the future leadership and political direction of the party, is if Labour MPs nominate me onto the ballot paper."