Lord Mandelson remains a close ally of Tony Blair
Tony Blair does want to be the first president of the European Council, his ally Lord Mandelson has told the BBC.
Mr Blair has made no public comment about the job, which will be created if the Lisbon Treaty comes into force.
But Cabinet minister Lord Mandelson said Mr Blair had told him he wanted the job but not so much "he couldn't live without it".
Gordon Brown is lobbying for Mr Blair but a lack of support from EU socialist leaders could scupper his chances.
The Lisbon Treaty came a step closer to coming into force during an EU summit in Brussels after EU leaders struck a deal with the Czech Republic - the last EU state to sign up to it.
At the summit French President Nicolas Sarkozy said he and German Chancellor Angela Merkel had decided on their own joint candidate.
In an apparent reference to Mr Blair, he added: "The first names to come out of the hat are not the ones that are finally chosen."
Mr Blair, currently a Middle East envoy, has not said publicly that he wants the job - his office says that as the job will not exist until the Lisbon Treaty is ratified, there is no clear job description yet.
But Gordon Brown and Foreign Secretary David Miliband have been arguing for his candidature this week.
In an interview with the BBC's Hard Talk programme, to be shown on Monday, Business Secretary Lord Mandelson said: "He would like to do the job. But when I talk to him, I don't feel it's a life or death question for him. He doesn't want it so much he couldn't live without it - but he's committed to it.
'He would be a very good candidate ... it's a new job and whoever does that job first is going to shape and define it for years to come.
"Now if we want that job to be a really influential job you are going to need someone with a good brain and a strong personality. Tony Blair has both."