The Daily Telegraph reported that Maugham said Johnson was saying two contradictory things at the same time.
"But there is plenty of time for the UK Government to put forward further proposals and we're in the process of trying to arrange a meeting between me and Prime Minister Johnson next week".
The document was revealed by Aidan O'Neill QC, the lawyer acting for campaigners who want judges to issue an interdict, or injunction, forcing the PM to delay exit day if no agreement is signed off by 19 October.
However, his government also acknowledged for the first time on Friday that Johnson will send a letter to European Union asking for a Brexit delay if no divorce deal has been reached by October 19.
No doubt Britains prime minister is capable of that kind of calculation.
Speaking to BBC Radio Scotland's Good Morning Scotland programme on Friday, she added: "We're not bringing this case because we think there's any loophole in the Benn Act".
Britain's current idea for an alternative to the backstop - which would see all the United Kingdom, or at least Northern Ireland, remaining in the EU's customs union - is for untried technology to remove the need for most but not all border checks, and for EU standards on goods to continue to apply in Northern Ireland to facilitate trade. The first element of Johnson's proposal is to continue to abide by the terms of the Good Friday Agreement that now governs the border between Ireland and Northern Ireland.
On a tour of Paris, Berlin and other capitals next week, Johnson will appeal directly to European Union leaders to support his new "compromise" plan, which he has described as a "fair" and "reasonable" offer.
Mr Tusk also spoke to Mr Varadkar on Thursday and delivered the message "we stand fully behind Ireland".
Mr Smith had earlier said reform of a contentious Stormont voting mechanism could be "helpful" in addressing concerns about handing the DUP a veto over post-Brexit arrangements.
A spokesman for Downing Street told POLITICO that "The PM has said that what we have to derive is derive a deal, and derive Brexit accomplished on October 31st with out any extra pointless prolong. It's a no deal budget so it has to be more conservative than previous budgets and what that means is no across the board income tax cuts and no across the board welfare increases", he said.
The Prime Minister's Europe adviser, David Frost, has been in Brussels for technical talks with officials.
With the clock ticking down to Britain's departure on October 31, Johnson has consistently said he will not ask for a Brexit delay, but also that he will not break a law that forces him to request one if no withdrawal agreement deal has been agreed.