Dominic Raab has suggested to MPs he “expects” a deal on the UK’s exit from the EU to be agreed by 21 November.
The Brexit Secretary said he was happy to appear before a committee of MPs scrutinising the Brexit process “when a deal is finalised” and “currently expected 21 November to be suitable”.
An agreement over the controversial issue of the Irish border was “not far” off, Mr Raab added.
No 10 said it was working to reach an agreement “as soon as possible”.
Officials said concluding a deal by the middle of next month remained an aspiration and there had been no major breakthrough in recent days.
The UK is due to leave the EU on 29 March 2019.
The two sides want an agreement on the details of the UK’s withdrawal and an outline plan for their future relations before the end of the year, to give the UK and EU Parliaments enough time to vote on it.
But the talks have stalled over how to prevent the return of physical checks on the border between Northern Ireland and the Republic of Ireland.
Plans for a special summit in mid-November to seal the withdrawal agreement were put on hold after insufficient progress was made at a meeting of EU leaders earlier this month.
High-level political talks between the two sides are currently on hold, although technical discussions continue to try and find a way ahead.
In his letter to Brexit committee chairman, Labour MP Hilary Benn, on 24 October, Mr Raab struck an upbeat tone.
He said the end of the negotiations was “firmly in sight and while obstacles remain it cannot be beyond us to navigate them”.
Despite differences over Northern Ireland, he said the two sides were “not far” from agreement over the terms of the so-called “backstop”, which could see the whole of the UK remain in a temporary customs arrangement with the EU until their future relationship was settled.
“An agreement on the details of that backstop should be possible,” Mr Raab wrote.
“We have resolved most of the issues and we are building up together what the future relationship should look like and making real progress,” he added.
In response to Mr Raab’s letter, Downing Street said “we are working to achieve a deal as soon as possible”.