Belgian Prime Minister Guy Verhofstadt will not be acceptable as the next European Commission president, several European Union leaders have made clear to the Taoiseach, Mr Ahern.
Up to now, Mr Ahern has retained hope that the Belgian could emerge as the replacement for Mr Romano Prodi during next weekend's European Council summit in Brussels.
However, the growing opposition to the Belgian, expressed forcefully to Mr Ahern during last week's G8 meeting in the United States, is increasing the pressure on the Taoiseach to take the post instead.
The name of the Taoiseach will feature as a compromise candidate in talks due to take place on Thursday between the United Kingdom, France, Germany and Italy.
However, the refusal of the Taoiseach to rule himself out of contention for the vacancy to be left by Mr Romano Prodi is causing increasing confusion among senior Fianna Fáil politicians.
In particular, Mr Ahern's repeated declaration that the Commission president's job is worth €1 million a year has been met with bafflement, since the post actually pays approximately €200,000 per year.
During an interview with the Sunday Tribune, which was conducted last week in the United States and published yesterday, Mr Ahern mentioned the higher salary figure three times.
Claiming that "50 per cent" of EU leaders had asked him to take the post, he went on: "You can never say no.
"But I don't see the circumstances arising. There is a clear favourite for the job."
Few of the Taoiseach's Cabinet believe that Mr Ahern is seriously angling for the job, though some quarters suspect that he could be using it as a device to deflect attention away from FF's local election result.
Sources close to Mr Ahern insist that he does not want the job, though he fears that he could come under strong pressure to let his name go forward during the Brussels summit.
However, there is a chance that the Luxembourg Prime Minister, Mr Jean Claude Juncker, who previously ruled himself out, could change his mind and put himself forward.
Despite Mr Ahern's continual assertions that his fellow prime ministers have lobbied him on the issue, none of them has chosen to put this support on the record.
The leadership of the Commission is expected to be officially decided by the European Council in Brussels on June 17 and 18th, although the issue is far from decided.
Belgian Prime Minister Guy Verhofstadt, despite his official denials, is known to be interested, though his federalist opinions would make it increasingly difficult for him to secure British support.
Austrian Chancellor Wolfgang Schuessel and Denmark's Prime Minister Anders Fogh Rasmussen have also been linked with the post.
Meanwhile, the former Socialist Greek prime minister, Mr Costas Simitis (67), could become a last-minute challenger, according to a left-wing Athens newspaper yesterday.