Theresa May is under pressure to set out when she will quit Number 10 after a Cabinet revolt over her Brexit plan.
The Prime Minister will meet the leader of backbench Conservatives, Graham Brady, today (Friday) to discuss her future after her authority was left in tatters following the backlash against her "new Brexit deal".
Senior ministers set out their concerns in "frank" talks with the beleaguered premier as Downing Street delayed publication of the Withdrawal Agreement Bill (WAB) which sets out her Brexit plan in law.
The Prime Minister's private meeting with Mr Brady, chairman of the powerful 1922 Committee of Tory backbenchers, could be the moment that Mrs May sets the date for her exit from Downing Street.
A 1922 Committee source told Press Association they expected June 10 to be the day Mrs May chooses.
"Hopefully what will happen is she will stand down as Tory leader I think on or before June 10, and she will hopefully remain as caretaker Prime Minister until such time as a new Tory leader is elected," they said.
"My feeling is that she will stay until June 10."
The source said a new leader would ideally be in place by the end of the European summer to get a Brexit deal through parliament before October 31, the date currently set for the UK's exit from the EU.
In Ireland, there are increasing fears that Mrs May’s departure will increase the chances of a hard Brexit, especially if she is replaced by a committed Brexiteer like Boris Johnson.
Tánaiste and Minister for Foreign Affairs Simon Coveney has ruled-out any renegotiation of the Withdrawal Agreement, which maps-out Britain's exit from the European Union, if Theresa May is replaced as British Prime Minister.
Speaking on RTÉ's This Week, Mr Coveney said: "It's not up for renegotiation, even if there is a new British prime minister...the personality might change here, but the facts don't."
He described Mrs May as "a decent person" but strongly criticised Conservative MPs at Westminster - branding them as "impossible" on the issue of Brexit.