The report claims an "all-UK customs deal" will be written into the legally binding withdrawal agreement, which would do away with the need for the controversial "backstop" arrangement agreed by the United Kingdom last December, which would see Northern Ireland remain in full alignment with the EU's single market and customs union rules in the event of a no-deal Brexit.
This would avoid the EU's "backstop" solution of treating Northern Ireland differently from the rest of Britain.
"He recalled the prior commitments made that the backstop must apply "unless and until" alternative arrangements are agreed".
"In order to ensure that the backstop, if ever needed, would be temporary, the prime minister said that there would need to be a mechanism through which the backstop could be brought to an end", the spokesman added.
Asked about the report, a spokesman at May's office said: "This is all speculation".
Varadkar separately told reporters that an expiry date of that nature would not be worth the paper it is written on.
The publication added that Mrs May's cabinet could be discussing the plans on Tuesday and are hoping to make enough progree by Friday for the European Union to announce a special summit.
An open frontier is seen as crucial to preserving the 1998 Good Friday peace accord that ended decades of Irish sectarian bloodshed.
The EU has proposed keeping Northern Ireland inside a customs union with the bloc to remove the need for border checks on the island.More news: Theresa May’s ‘secret Brexit deal’ with EU
Parliament would then vote on the deal in December. In the 2016 referendum, Britons voted 52-48 per cent in favour of Brexit.
Simon Coveney, the Irish foreign minister, made clear on Monday morning that this would never be agreed.
Brussels is preparing to back a compromise proposal on the backstop to resolve the last big sticking point in the Brexit negotiations.
She urged him to "show leadership" and not "leave behind" the people of Northern Ireland.
But London and the European Union have still not agreed how long such an insurance policy would last.
Britain remains optimistic that agreement can be reached at an European Union summit at the end of the month, but has ruled out a breakthrough within the next week.
While European Council President Donald Tusk said in September that an extraordinary summit would be called for November 17-18 to finalize and formalize the EU-UK arrangement if sufficient progress in talks was reached, the EU leaders are now not planning this extraordinary summit.
Speaking at a meeting of the British-Irish Intergovernmental Conference in Dublin, Mr Coveney said he believed "it is possible to get a deal in November", adding: "This border issue is complicated to resolve. but I think we're very close to resolving it".
The UK statement did not refer to the Irish position that the mechanism could not involve a unilateral decision to end the backstop.