Ireland's prime minister has told Theresa May in a hastily arranged phone call that he cannot allow the United Kingdom to unilaterally decide when to terminate the Irish backstop, creating the possibility that Britain could be tied in a customs union with the EU for the long term.
"The (British) Prime Minister raised the possibility of a review mechanism for the backstop", the spokeswoman added.
Ms O'Neill commended the letter signed by 1,000 nationalists across Ireland to Mr Varadkar, urging him to defend the rights of Irish citizens north of the border amid uncertainty caused by Brexit and Stormont's political crisis.
If he does, other senior ministers anxious about her proposals will also get behind the deal, a person familiar with the matter said.
It is speculated that May is hoping for enough progress in Brexit talks this week to secure a summit later this month in which the final details of a deal will be negotiated.
According to the Sunday Times, the agreement would include an "exit clause" aimed at convincing Brexiteers that remaining in the customs union would be temporary.
A spokesperson said: "The prime minister has been clear that we are making good progress on the future relationship and 95pc of the Withdrawal Agreement is now settled and negotiations are ongoing".
The former Labour Prime Minister, Tony Blair, an active supporter of Britain remaining in the European Union, urged all MPs Sunday to vote down whatever Brexit deal May presents to parliament, and should instead push for another referendum. After meeting on Friday with Irish Deputy Prime Minister Simon Coveney in Dublin, British Prime Minister Theresa May's deputy David Lidington said negotiators were "very close" to an agreement. Alternatively, it is proposed to establish in Northern Ireland a free customs zone, which, in turn, resent the EU.
The key sticking point remains how to avoid customs checks taking place at the border between Northern Ireland and the Irish Republic, without putting up new barriers between Northern Ireland and the British mainland.
The former attorney general told BBC Radio 4's Today programme: "At the end of the day it highlights why the entire enterprise is questionable, because in fact what we are likely to end up with is leaving the European Union but staying in a relationship of sufficient dependency on it without influence as to call into question the whole project".
But the government's Brexit department stated that they are confident there will be a deal that works for businesses - and reiterated their stance against a People's Vote.