Labour is likely to put forward somebody of the calibre of Education Minister Ruairi Quinn, according to sources.
Taoiseach Enda Kenny is expected to reshuffle his Cabinet at the halfway point of the Government's five-year term next autumn.
Health Minister James Reilly is thought to be number one in the firing line.
He has already faced one no- confidence vote in the Dail, lost a junior minister and is expected to be hit by another confidence vote in the new year.
Rumours that Mr Kenny was considering a reshuffle in early 2013 have been ruled out by ministers, who say the timing would be all wrong.
"The Government will just be over a very difficult Budget and dealing with the EU presidency. The last thing that would be needed before the summer recess would be more scope for instability or friction," said a source.
Ms Geoghegan-Quinn, who was appointed as our European Commissioner in 2010, is due to leave the post in 2014.
This means Mr Kenny could drop one of his big names from Cabinet late next year, with the promise of the top post.
"At the minute Phil Hogan would be to the forefront of minds in Fine Gael, but it depends on whether he would want the job. The Taoiseach is not going to ship 'Big Phil' off to Europe in the same way Ahern dealt with Charlie McCreevy in 2004," said a source.
However, they noted that Labour would have some say in deciding who would get the job, which comes with a salary of around €250,000.
Tanaiste Eamon Gilmore would be likely to nominate Ruairi Quinn, although it is likely that the Coalition will try to reach an early compromise on the candidate.
But Mr Kenny's biggest problem is what to do with Dr Reilly. In the event of a reshuffle Labour will be expected to push hard to move him from the Department of Health, but then face the question of who to replace him with -- and where to send the Dublin North TD.
"Nobody will want to lose face," said a source.