Minister for Social Protection Joan Burton is likely to put herself forward for the Labour leadership.
She is widely expected to put herself forward for the job within the next 48 hours.
Mr Gilmore announced yesterday he was stepping down, in the wake of the weekend's disastrous election results.
The leadership is likely to be the main talking point at this morning’s Cabinet meeting.
It’s the first time Labour and Fine Gael ministers will have met since yesterday’s announcement - with the stability of the Government among their main concerns.
The Tánaiste’s surprise resignation caught Ministers off-guard yesterday afternoon - and for Fine Gael members of Cabinet at least raised some questions about the stability of the coalition.
They’ll have the chance to ask Eamon Gilmore and his Labour ministers about the impact of his decision when they meet here at Government Buildings this morning.
Social Protection Minister Joan Burton has already emerged as the frontrunner for the party leadership - and is known to have contacted Labour TDs seeking their support just hours after Mr Gilmore’s announcement.
Public Expenditure Minister Brendan Howlin and Junior Health Minister Alex White are also thought to be considering whether to contest July’s leadership vote.
However, the main question for Fine Gael ministers will be over the stability of the coalition - and how to refocus both parties as they look to bounce back from poor performances in the local and European elections.
