Fine Gael Leader Enda Kenny is expected to leave some time before taking decisions on frontbench positions after his victory in yesterday's confidence vote.
Mr Kenny is likely to include some TDs who opposed him but major changes are inevitable.
Names being linked to the Deputy Leader post include Health Spokesman Dr James Reilly and Environment Spokesman Phil Hogan.
Former leader and Government Minister Michael Noonan has been tipped to take over the finance portfolio from leadership challenger Richard Bruton.
Those who may expect promotion include Alan Shatter, Paul Kehoe, Jimmy Deenihan and Michael Ring.
A number of Mr Kenny's opponents said earlier this week that they would not serve under him if he won the vote.
Simon Coveney, Leo Varadkar and Fergus O'Dowd, who had opposed Mr Kenny, conspicuously accepted the result of yesterday's vote.
Speaking on RTÉ's Morning Ireland, Wexford TD Michael D'Arcy, who opposed Mr Kenny, said support for the leader was now unconditional following the vote.
Some former dissidents are sure to find their way into the new shadow cabinet, although any announcement may have to wait for a week or two.
Taoiseach Brian Cowen has said that he wished Enda Kenny well and that they would continue next week where they left off.