There is also the suggestion that he will step down after Northern Ireland's assembly meets next Tuesday, bringing to a close the political process that Mr Blair has worked on for many years.
The prime minister told GMTV: "I'll make my position clear next week. I'll say something definitive then.
"Ten years is a long time to do this job and I think it's right that it's a fresh team that takes over now."
Asked how he would rate Gordon Brown as chancellor out of ten, Mr Blair remarked that he would give him top marks.
"I've always said about him that he would make a great prime minister and I believe that," he said.
Mr Brown is the frontrunner in the impending Labour leadership election which will commence once the prime minister has stated his intentions.
Currently only two other Labour MPs - Michael Meacher and John McDonnell - have said they will challenge Mr Brown.
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