He will be nominated by EU leaders in Brussels if, as expected, Ireland backs the hated Lisbon Treaty in tomorrow's referendum.
A senior Government source said: "If we get a 'Yes' vote it will all move very, very quickly. Tony could be named by the end of October."
The leaders of the EU's 27 nations, not the voters, will choose the president.
Former PM Mr Blair would not formally take up the powerful position until all EU countries ratified the Treaty.
Even if Ireland votes "Yes", Poland and the Czech Republic are still to decide. But Sweden, which currently holds the EU presidency, wants a president named by the end of this month - and Mr Blair is favourite.
Asked if Mr Blair was the only real candidate, French Foreign Minister Bernard Kouchner replied: "For the moment, indeed."
A senior French diplomat added: "Who will dare say no to Tony Blair?" He played down concerns about Mr Blair's support for the Iraq War.
Art's Commentary.....The new President of the EU could be the Antichrist, though he will not be known until after the church is raptured. This new President will be given unprecidented power over the EU nations. This certainly will be the office which Antichrist will occupy. The pace is quickening in the preparations for the final drama of the age which seems soon to begin. In every area of endtime Bible prophecy the same quickening pace is evident. This perhaps is our last opportunity to sound out a warning to a world about to fall under the Day of the Lord Judgment. Though we do not know the day nor the hour, it seems we are at the very doors of the calling home of the church. Some will be ashamed at his appearance, let us be ready and watching. The prophet said "Arise and be doing and the Lord be with thee".