Enda Kenny is facing pressure from all directions to say when he will step down as Taoiseach.

His own party have suggested he will face a motion of no confidence if he does not set out a clear plan.

"He will signal in the next short time his intention to step down - probably next week. He'll see the writing on the wall", Newstalk Breakfast presenter Shane Coleman says.

"He will have to set out a concrete time frame".

"But it could be a long handover to the new leadership election", Coleman cautions. He suggests it could be May before a successor is chosen.

However, Mr Kenny becomes the longest serving Fine Gael Taoiseach on April 26th - with suggestions he may still be leader then.

This will potentially mean his last big public engagement is the trip to Washington, DC for St Patrick's Day.

But internal party pressure means he will have to have his time frame in place well before that date.

TDs are warning he will face a motion of no confidence at the Parliamentary Party and a heave next week, if he does not indicate when he will step down.

His party colleagues hope that over the weekend he will work out a plan and announce it before Tuesday.

Leo Varadkar (front) with Taoiseach Enda Kenny opening Irish Sport HQ | Image: RollingNews.ie

And who will take the reigns of Fine Gael?

"It will largely be the Parliamentary Party that decides", Coleman says - with Minister Leo Varadkar seen as a clear favourite.

While Mr Kenny himself appears to have admitted his time as Fine Gael leader is coming to an end.

Finishing up an appearance before the Oireachtas Finance Committee on Thursday, chairman John McGuinness said: "I know that these are difficult times and I want to wish you well, personally".

Mr Kenny simply replied: "C'est la vie". His appearance was for routine business relating to the 2017 budget for his department.

Speaking in Dublin on Thursday, Mr Varadkar said the Taoiseach will know when the time is right to go.

"Enda Kenny has been a fabulous leader of Fine Gael for the past 15 years - the events of this week show that the timeline for a general election is now shorter than we might have thought.

"The Taoiseach has said that he won't lead us into the next general election, but I've absolutely every confidence that he'll know when the right time is - for himself, for the party and for the country - to step aside".

While speaking on Wednesday, Fine Gael Dublin North-West TD Noel Rock said things need to change.

"Most Irish people don't want an election right now" he said, before adding that he believes the Government is "potentially tipping towards an election".

Mr Rock also said he wants to see Mr Kenny to set out a timeline for when he will step down.

"In my opinion, Leo (Varadkar) and Simon (Coveney) would represent a good generational change," he told Newstalk.com.

While betting website Paddy Power say Mr Varadkar is the favourite to become the next leader of Fine Gael.

Following him is Simon Coveney, Paschal Donohoe and Richard Bruton.

Additional reporting: Páraic Gallagher and Sean Defoe