Irish Prime Minister Enda Kenny is expected to give his Fine Gael parliamentary party a timeframe for stepping aside when they meet later.
It is believed Mr Kenny will stand down shortly after meeting President Trump in Washington for the annual St Patrick's Day shamrock presentation.
There had been speculation he would face a motion of no confidence at Wednesday night's meeting
However, it now seems unlikely that will happen.
The speculation was that a no confidence vote would result from his handling of a police whistleblower controversy.
The controversy began more than three years ago when two whistleblowers - Sgt Maurice McCabe and the now retired John Wilson - alleged there was widespread corruption with the Republic of Ireland's driving licence penalty points system.
A public inquiry is to be held into whether Sgt McCabe was falsely smeared by senior officers in the An Garda Síochána (police).
There will also be an independent review of police operations.
Last week, the Irish coalition government - which is made up of Fine Gael and the Indepenent Alliance - survived a vote of no confidence in the Irish parliament (Dáil).
The government won the motion by 57 votes to 52 votes and there were 44 abstentions.
Sinn Féin tabled the motion over the handling of false sex crime allegations against the police whistleblower Sgt McCabe.
The party accused the government of covering up "who knew what and when."
The Fine Gael leader was re-elected as taoiseach (prime minister) in May 2016, 70 days after a general election which had produced no outright winner. He was the first Fine Gael taoiseach to be re-elected to office after a general election.
Mr Kenny became leader of Fine Gael in 2002 and was first elected taoiseach in 2011.