The former British prime minister's name was put in the frame this weekend by Nicolas Sarkozy, the French president, who described Blair as "a very remarkable man . . . the most European of all Britons". He added: "To think of him would be a good idea."

The treaty scraps the current system under which one country holds the EU's rotating presidency for six months. It will be replaced by the appointment of a president, who will chair EU meetings, drive through its agenda and serve for two-and-a-half years.

Gordon Brown said: "Tony Blair would be a great candidate for any significant international job." He added: "As you know the work that he is doing in the Middle East is something that is of huge international importance."

But he said it was premature to speculate on who might fill the post because the appointment would not be made until the treaty had been ratified by member states next year.

There are several obstacles to Blair's securing the post. Although he is regarded as a heavyweight in EU capitals, he is also remembered as the man who divided Europe by giving George Bush such strong backing for the 2003 invasion of Iraq. Some EU diplomats predicted that he would not secure enough support from member states.

Friends doubt Blair would even want the job. The new president would not be as powerful as the title or the 300,000-a-year salary suggests. He or she would help to shape the EU's agenda and be seen as the EU's representative on the world stage. But the key decisions would still be taken by national leaders from member states.

After standing down as prime minister in June, Blair became the Middle East peace envoy for the Quartet . . . the US, Russia, the UN and EU. His spokesman did not rule out his taking up the new EU post but said: "He is focusing on his current role in the Middle East."

Other potential candidates for the post include Taoiseach Bertie Ahern and former Polish president Aleksander Kwasniewski.