The Taoiseach is due to name the new Tánaiste later today.
It follows Tuesday's resignation of Frances Fitzgerald from the role.
Simon Coveney was Leo Varadkar's opponent in the battle to lead Fine Gael, but the Foreign Affairs Minister has been a favourite to be named as Tánaiste in the Dáil today.
The Cork-based minister would help offer regional balance in Cabinet leadership - with Mr Varadkar from a Dublin constituency.
Minister for Culture, Heritage and the Gaeltacht Heather Humphreys is also believed to be in the running.
The appointment of the Cavan-Monaghan TD would ensure a gender balance in the top two roles, and could help boost support in the border counties.
Other potential 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 Mr Varadkar has been criticised for the gender imbalance in his Cabinet, there is speculation the next holder of that portfolio will also be female.
Deputy Fitzgerald's decision to stand aside came after a week of criticism from opposition parties over her handling of an email in May 2015 which alluded to the Garda legal strategy against whistleblower Maurice McCabe.
A Fianna Fáil motion of no confidence in the former justice minister had threatened to bring an end to their confidence & supply agreement with Fine Gael - which would have seen the collapse of the minority Government.
However, Deputy Fitzgerald's decision on Tuesday to resign - only hours before the Fianna Fáil motion was due to be debated - averted a Christmas election.
Reporting by Sean Defoe, Stephen McNeice and Tom Swift