Senior Fine Gael figures believe Enda Kenny will quit as party leader within days as he faces the unedifying prospect of a no confidence motion, writes RTÉ's Mícheál Lehane.

The Taoiseach indicated yesterday at his parliamentary party meeting that the leadership issue could be discussed next week but many want it dealt with immediately.

However, a request by Minister for Social Protection Leo Varadkar to bring forward the timing of the next parliamentary party meeting was not agreed to.

Party Chairman Martin Heydon said a meeting would take place at the usual time in Leinster House next Wednesday.

It’s being viewed as highly significant that the two leading contenders to replace Mr Kenny, Simon Coveney and Mr Varadkar, both addressed the meeting with an almost identical message.

It was a simple and direct one: the party needed to be ready for an election from now on.

It was taken as a coded warning to the Taoiseach to prepare to depart office given that he has made it clear he will not lead the party into the next election.

And indeed this coded language was given voice after the meeting by some of those once regarded as the Taoiseach’s most loyal supporters.

The apparent act of co-operation between Mr Coveney and Mr Varadkar has led some in the party to question if both men have a tacit agreement in place that guarantees the defeated candidate the job of Tánaiste.

One way or the other it has had the effect of the quickening those inexorable moves against the Taoiseach should he fail to announce his departure plans.

"The next few days will tell a lot but it’s looking increasingly likely that this will be wrapped up very quickly. He will be given an ultimatum privately today by the heirs to the throne and the rest of the party will follow if he doesn't go," said one Fine Gael TD.

It is also expected that some of Mr Kenny's senior ministers, who have been given assurances about their place in a reshuffled cabinet under any a new leader, will soon openly speak about the need for the Taoiseach to signal his intention to step down.

This will mean though that the anticipated Cabinet clear-out will not be as extensive as was first thought by party backbenchers.

But it’s likely Finance Minister Michael Noonan will be one of those forced to exit office.

"I don’t think he’ll even get time to collect his coat. He tried to say at the PP meeting that only himself and the Taoiseach could handle the Brexit negotiations but he was just scoffed at," a party TD said.

Others such as Jobs Minister Mary Mitchell O’Connor, Foreign Affairs Minister Charlie Flanagan and Agriculture Minister Michael Creed are set to remain in any new cabinet.

While Education Minister Richard Bruton, Public Expenditure Minister Paschal Donohoe, Health Minister Simon Harris and Chief Whip Regina Doherty seem certain to be senior figures under any new leader.

The futures of the Justice Minister Frances Fitzgerald and the Arts Minister Heather Humphreys are unclear right now.

Under the Fine Gael constitution the election of a new leader must be completed within 20 days of a vacancy arising.

The result will be decided by TDs, Senators, MEPs, party members and councillors.

Additional reporting Pat McGrath

Fine Gael members in the Taoiseach's constituency are still hopeful he will be given time to make his own decision regarding the timing of his departure from office.

While many admit that Enda Kenny faces serious challenges in the coming days, they are expressing the view that he should be afforded space to decide on when he will step down as leader.

Castlebar based Fine Gael Councillor Cyril Burke said the parliamentary party needed to think seriously about the impact a move on Mr Kenny could have.

He said the Taoiseach was best equipped to deal with the many challenges posed by Brexit and deserved to be allowed determine the timeframe for leaving office.

Cllr Burke said that he would not write off the Taoiseach at this stage, saying he was at his best when his back was to the wall.

He expressed the view that he could use next week's Fine Gael Parliamentary Party meeting to stress the importance of stability at this time.

Those sentiments were echoed by former Fine Gael Mayor of Castlebar Brendan Heneghan, who said "the fat lady has not yet sung".

Long-standing party member Tom Collins said he felt that the Taoiseach would remain in office until he was certain that the stability of the country was secured.

He suggested that while some leadership contenders wanted a date for Mr Kenny's departure, they were less interested in assuming the top job at this point in time.

There's agreement that any decision by the Taoiseach would be taken following consultation with a very limited circle of people.

Several party members expressed the view that adversity brought out the best in Mr Kenny and some went as far as to suggest that he might try and face down a motion of no confidence, were one to be tabled.