The news comes after a former Government whip warned the Prime Minister she was unlikely to get her blueprint through Parliament, as the pressure mounts with less than six months before the UK quits the bloc on March 29, 2019.
Mrs May will meet with ministers on Tuesday to discuss Britain leaving the EU – the day before she heads to the Belgian capital, with the key sticking point, the question of the Irish border, at the top of the agenda.
In a move certain to incur the wrath of Brexiteers such as Boris Johnson and Jacob Rees-Mogg, Mrs May is expected to push for a commitment to keep the whole of the UK in what would effectively be a customs union with the EU, but setting a path via which it will be able to exit such an arrangement, The Times reports.
Support within Mrs May’s cabinet is lukewarm, wit Jeremy Hunt, the foreign secretary, Sajid Javid, the Home Secretary, Dominic Raab, the Brexit secretary, and Michael Gove, the environment secretary, backing Mrs May for the moment – but coming round to the idea of a Canada-type deal if the Chequers plan gets the cold shoulder from the EU next week.
Work and pensions secretary Esther McVey, international development secretary Penny Mordaunt, and leader of the House of Commons Andrea Leadsom, all of whom campaigned for Leave in the 2016, would be deeply unhappy with any further compromises, having avoided endorsing the Chequers proposals as they stand.
Former Brexit secretary David Davis has already told Tory Parliamentary colleagues they would face a battering at the ballot box if they stick with Mrs May’s Chequers plan.
He rejects Mrs May’s suggestion that MPs face a choice of Chequers or no deal, insisting a third way does exist.
Meanwhile, in column written for The Telegraph, former chief whip and May loyalist Mark Harper warned the Prime Minister she would not be able to get her White Paper based on her Chequers proposals through Parliament.
He said: “Get 25 Labour MPs to vote for Chequers? I think that would be very optimistic.
“I don’t think more than a handful of Labour MPs would vote for it, if that.
“There’s a considerable number of Conservative colleagues who’ve been explicit that they aren’t going to support Chequers.
“Given that our working majority with the DUP’s support is only just into double figures, you only need a handful of colleagues for this not to get through Parliament.
“Clearly the proposals need to evolve.
“If they evolve in a Canada direction then the Prime Minister will have something she can unite the party around and get through parliament.
“If they evolve in a more Norway direction, I think she’s got less chance of getting it through.”
Other Tory MPs have also been casting doubt on Mrs May’s plans in recent days, with several retweeting Mr Harper’s article.
However, Mr Raab tweeted yesterday evening: “Today, I updated MPs on both our Brexit negotiations with the EU, and our latest No Deal planning.
“We continue to strive for a good deal with our EU friends – but we’ll be ready to make a success of Brexit, in any eventuality.”
Earlier in the day, Mr Raab had been pressed by Labour’s Brexit spokesman Keir Starmer about the suggestion that the UK would stay in a customs union indefinitely after Brexit, insisting: “No, categorically that is not correct.”
His words pile added pressure on Mrs May to strike a deal which would set a date by which the UK would be free from such a system.