Mr Blair has not publicly commented on whether he wants the job
Tony Blair's hopes of becoming president of the European Council are fading after his supporters failed to secure the backing of EU leaders.
Gordon Brown said Mr Blair would make an "excellent president" but there were "many candidates who may come forward".
Meanwhile ratification of the Lisbon Treaty, which creates the post, moved closer after EU leaders struck a deal with the Czech president.
Mr Brown said they had cleared the way for the treaty to be ratified.
No 10 has signalled that a defeat for Mr Blair's candidacy is now "a clear possibility".
The former British PM has not declared himself a candidate but British ministers, including Mr Brown who is at a meeting of EU leaders in Brussels, have been talking him up for days.
Speaking at the end of the summit, Mr Brown said: "I think I am right to say that Britain has someone in Tony Blair who would make an excellent president of the Council of the European Union.
"I think there are many people who are members of the council who accept that and believe that to be true."
Gordon Brown reiterates his support for Tony Blair as President of the EU Council
But he added: "I recognise also that there are many candidates who may come forward, some have already indicated their intention to do so, but I do believe that Tony Blair will remain an excellent candidate."
At the summit EU leaders agreed to grant the Czech Republic, the only EU state not to have signed up to the treaty, an opt-out from the EU's Charter of Fundamental Rights.
Mr Brown said he believed that the meeting had "cleared the way" for the Czech Republic to ratify the Lisbon Treaty - should the country's constitutional court rule in its favour next week.
Once that happened European member states would discuss the position of the presidency and the commissioners, he said.
If it is ratified it will also increase pressure on the Conservatives - who oppose the treaty and say there should have been a referendum on it - to spell out what they will do if they win power and it has come into force.
Conservative leader David Cameron told the BBC: "If that comes to pass we'll set out straight away what our approach to that important issue will be."
The BBC's Jonny Dymond in Brussels said Mr Blair's chances of becoming the first president of the European Council - a post created by the treaty - seemed "slimmer today than before".
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.