The Taoiseach is expected to nominate Ireland's next EU Commissioner within the next two weeks. Mr Ahern will discuss the matter next week with the EU Commission President, Mr Romano Prodi.
Mr Prodi has said he would like a senior serving politician - in other words a member of the Cabinet - and a woman. Mr Ahern appears almost certain to give him one or the other, but not both.
Government sources say they believe Mr Ahern is giving serious consideration to appointing a Cabinet member. The threat of a defeat in the resulting by-election is not as major a factor as has been suggested, say these sources.
The Cabinet Ministers most frequently mentioned as possible nominees are Mr Brian Cowen and Dr Michael Woods, with Mr Joe Walsh, Mr Noel Dempsey and - in some circles - Mr Dermot Ahern also being suggested.
There is no obvious front-runner.
Ms Mary O'Rourke has let it be known that she is not interested, while the only other woman Cabinet member is the Tanaiste, Ms Harney. With the Commissionership believed certain to go to a Fianna Fail member, both she and her party colleague, Ms Liz O'Donnell, would be ruled out.
Mrs Maire Geoghegan Quinn is the most regularly mentioned among non-ministerial candidates. She was until 1994 a senior prominent serving politician, and her appointment would avoid a by-election.
Mr Ahern's relationship with Mrs Geoghegan-Quinn - once frosty and distant - has improved significantly in recent years.
PD acquiescence in a Fianna Fail nomination for the Commissionership would be seen as a good investment in securing the impending post on the European Court of Auditors for one of their own. This very well paid Luxembourg-based job will become vacant early next year as the incumbent - Labour Party appointee Mr Barry Desmond - has said he will not seek a second term.
The former PD leader, Mr Desmond O'Malley, is mentioned as a possible candidate.
However, even if PD opposition dissipates, there would be a lack of enthusiasm for Mrs Geoghegan-Quinn from some Ministers who feel she is not "owed anything" by the party, and should not be handed such a "plum" job.
Others say she would represent the party and the State well, and point out enthusiastically that her appointment would have no effect on the Dail arithmetic.
Sources close to Mrs Geoghegan-Quinn say she does not need the job, and has not campaigned for it. They say she is happy and content in her present life, working as a consultant and as a director of several companies - including Aer Lingus and Ryan Hotels. It is said that she should not risk this for a job she first wanted seven years ago, when it went to Mr Padraig Flynn.
Several senior party figures have discussed the Commissionership with the Taoiseach in the past week. Mr Ahern has listened, but said nothing.