The Taoiseach Leo Varadkar is due to name the new Tánaiste later today.
It follows Tuesday's resignation of Frances Fitzgerald from the role.
He was Mr Varadkar's opponent in the battle to lead Fine Gael, but the Foreign Affairs Minister Simon Coveney was an early favourite to be announced as Tánaiste today.
Waterford Junior Minister John Halligan said Minister Coveney was involved in critical Brexit negotiations, but the odds were in his favour.
Also hotly tipped is Minister for Culture, Heritage and the Gaeltacht Heather Humphreys.
Further back in the field contenders include Finance Minister Paschal Donohoe and Housing Minister Eoghan Murphy.
The departure of Frances Fitzgerald from the Cabinet also leaves the Taoiseach with the Business, Enterprise and Innovation role to fill.
Given that he has been criticised for the gender imbalance in his Cabinet, there is speculation the next holder of that portfolio will also be female.
