There would be an "exit clause" from the customs union in a bid to convince Brexiteers that it is not a permanent arrangement as May looks to secure votes to get the deal through Parliament, added the paper.
"I am extremely confident we will reach an imminent deal", Glen told a financial services conference in London.
The Sunday Times reports that the prime minister is close to a political deal on the United Kingdom and EU's so-called future economic partnership, which the newspaper says will "allow Britain to keep open the prospect of a free trade deal resembling that enjoyed by Canada".
Downing Street claimed the report about the deal is "all speculation".
"The Democratic Unionist Party is rightly anxious about the future of the Union and many Conservatives are too".
Theresa May has stated repeatedly she will not accept any formulation of the insurance policy to maintain an invisible Irish border if it means Northern Ireland alone remaining in the EU's customs union.
Insisting that negotiations are "ongoing" at a technical level, the Commission's chief spokesman summed up progress by telling reporters: "Not there yet".
At the same time, it reported that the prime minister was on course to agree a future economic partnership that would leave open the possibility of Canada-style free trade deal sought by Brexiteers.More news: Leroy Sane responds to weird Man Utd transfer rumour
According to the Telegraph, May has included Attorney General Geoffrey Cox, the government's chief legal adviser, in her special Brexit Cabinet after ministers said they wouldn't sign off on a deal without his advice. "We hope a deal can be done but we're not there yet". The government has previously said the withdrawal agreement is 95 percent complete and that there's also been progress in talks on the future relationship.
Cabinet minister James Brokenshire rejected suggestions that final agreement has been reached, saying negotiations are "still very firmly continuing", with 95% of issues resolved.
Following a phone conversation with Mrs May on Monday morning, the Taoiseach said both leaders emphasised their commitment to avoiding a hard border in Ireland and the need for a legally operable backstop.
"This is the backstop", he added, saying the United Kingdom had agreed that it would apply "unless and until" a close future relationship eliminated any need for Border infrastructure and checks.
The UK is looking for an agreement based on an improved version of the EU's "equivalence" system of financial market access.
Chief Executives from Waterstones, Innocent Drinks and Lastminute.com stated that the United Kingdom faces either a "blindfold or a destructive hard Brexit" in the note.
"I would have thought there will be quite a lot of Labour MPs in the Midlands, in the north, south Wales, sitting in seats where there was a big leave majority and by voting for May's deal they can say to their constituents "I voted for us to leave the European Union" even if the detail means we haven't really".