Tony Blair's hopes of becoming Europe's first sitting president were receding fast last night as Britain admitted his chances of success were "fading" after the continent's centre-right leaders made it clear one of their own must have the post.

Hours after Gordon Brown delivered his strongest statement of support for Blair – disclosing that he had spoken to him earlier this week – British sources indicated that the former prime minister was unlikely to assume the high-profile job.

"It would be right to describe Tony's chances as fading," one source said. "Nicolas Sarkozy and Angela Merkel are not terribly enthusiastic. Silvio Berlusconi remains his strongest backer."

Blair's expected failure to secure the post of president of the European Council meant that David Miliband was emerging as a serious contender to assume the new post of high representative for foreign policy. The foreign secretary insisted that he was "not available".

Miliband spoke out as British sources said it had become clear in recent days that Blair would struggle to become president. The post is likely to be filled in the next month as the Czech Republic inches closer to ratifying the Lisbon treaty after EU leaders agreed last night to include Prague in a protocol saying that the charter of fundamental rights does not create new rights.

Sarkozy, the French president, and Merkel, the German chancellor, discussed the new EU president at a dinner at the Elysée palace on Wednesday. They are understood to have agreed that the post should be filled from the main centre-right EPP grouping, which brings together the parties currently ruling most EU countries.

The French made clear in Brussels last night that Blair was losing their support. Jean-David Levitte, Sarkozy's most senior foreign affairs adviser, said: "The UK is not in the eurozone, nor in the Schengen [free travel area in the EU] and it has a number of opt outs. These are not advantageous in this search for a candidate."

Levitte indicated that Sarkozy was looking for someone who could combine the role of a chairman of meetings of EU leaders and representing the union on the world stage. "The ideal is to find a rare bird who can carry out the two functions, because we want an efficient Europe with strong institutions," he said in remarks which appeared to undermine Blair, who is seen as a world figure, not a chairman.

Brown hinted that Blair's candidacy was fading when he qualified his strong backing for his predecessor by saying that there were also other candidates for the job. "Of course it may not happen; there are other candidates as well," he said.

The prime minister's remarks came after an acrimonious meeting of European centre-left leaders. Brown was understood to have had a tense exchange with Martin Schulz, the German leader of the Socialists in the European parliament, who wants the left to assume the EU's new foreign policy post, leaving the presidency to the centre right.

Brown told the meeting: "You need to get real. This is a unique opportunity to get a progressive politician to be the president of the council."

But it soon became clear that Blair had no support on the left, let alone on the centre right. José Luis Rodríguez Zapatero, Spain's centre-left prime minister, for the first time publicly queried the Blair candidacy by announcing that the centre left across the EU was more concerned with securing the other post of European foreign minister.

Zapatero, who will have to work with the new European figureheads when Spain assumes the EU's six-month rotating presidency on 1 January, said: "There is a preference for the high representative. That is rather reasonable."

Jean Asselborn, Luxembourg's foreign minister, said: "Now in the United States, Obama is the president, it is no more Mr Bush. We have a new treaty, we have to reset Europe and we need to start with some new ideas. There is and will remain a link for the next generation between Iraq, Bush and Tony Blair."

Downing Street will resist criticism that it was wrong to mount such a strong campaign in favour of Blair after it had become clear earlier this week that his chances were fading.

Brown believes it was in the national interest to argue strongly as long as there was a chance to secure such a senior post for the country.

Brown said: "His international experience is well known, his expertise on environmental, economic and security issues is well known … If you have the chance for that to happen, it is in Britain's national interest."

His comments came despite signs that Blair has little support among the British public for the EU post. Of 50 Labour backbenchers who responded to a Guardian survey, 35 said they backed the former prime minster for the role and 15 did not. A YouGov poll for the Daily Telegraph found 31% of voters support Blair for president, with 31% opposed and 38% undecided.