His return to the global stage would be a shock to his critics over the Iraq war and dismay many in Europe.
But The Independent on Sunday has learnt that Mr Brown has accepted that his old rival should be in pole position for the appointment, on the basis that Britain needs to have a key figure in the architecture of the "new world order".
A senior British official said: "He [Brown] will have to swallow hard to sit down in meetings once again with Blair. But he accepts that there needs to be someone from the UK in the new global architecture. There is no opposition to the plan. Things have moved on, people have moved on."
Other European leaders are also broadly supportive because they want a high-profile figure to represent the 27-nation bloc in the new alliance with the US administration. Mr Blair remains a popular figure in the US.
After initially trying to block Mr Blair as a possible candidate last year, the French President, Nicolas Sarkozy, has thrown his weight behind the former prime minister.
As the eyes of the world were on London's G20 summit last Wednesday, Mr Blair held private talks with the European Commission President José Manuel Barroso in Brussels. The talks focused on his work as Middle East envoy to the quartet of world powers, but it is almost certain that the two men discussed his candidacy. The former premier also visited Sweden last week, where he shared a platform with Bill Clinton at a climate change conference.
The presidency job is dependant on Ireland voting "yes" to the Lisbon Treaty, which creates the position. The Irish referendum will take place in the autumn.
But Mr Blair's plans could still be scuppered if Angela Merkel loses the German general election in September. She is thought to have a strong desire for the job in the event of defeat.
Britain has already thrown its weight behind Mr Barroso to serve a second term as Commission President. His re-appointment would also strengthen the chances of a British name for the new job.
Mr Blair will have spent two years in the Middle East role by July, giving him a legitimate opportunity to claim he has devoted enough time to the job.
But critics will say Mr Blair has failed to make any significant breakthrough. There is also little chance of progress towards the two-state solution under the new hardline Israeli government led by Binyamin Netanyahu.
In a sign that Mr Blair's mind is on an exit from the Middle East, he said in Brussels: "I think the next six months will be completely critical in determining whether this process will move forward or whether it will slip back. I do believe that if there is not significant progress in the year 2009, the peace process will be in very great jeopardy, because there are decisions that have to be taken."