But speaking to the BBC today, Mr Miliband said that he is "not a candidate".
"Well I've not wavered in my view over the last three years and I'm not wavering now," he said in an interview.
"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."
Although questioned on Mr Miliband and his potential future in the Labour party, the prime minister refused to be drawn into speculation this afternoon.
When asked at his monthly press briefing if he had any advice for the environment secretary, Mr Blair said: "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.
"If I even raise an eyebrow out of place it is over-interpreted. So, I've got nothing to say on that," the prime minister added.
A number of senior Labour MPs have expressed their support for Mr Miliband, including John Reid, Charles Clarke and Alan Milburn.
Reports claim that despite his expressed intention not to challenge Mr Brown, his supporters could nominate him for the leadership via the Labour party website.
So far two politicians have announced their intention to run for the leadership; the left-leaning Michael Meacher and John McDonnell.
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