Brexit Secretary Dominic Raab has indicated that he expects a deal on Britain’s EU withdrawal to be finalised by November 21.
Downing Street has so far said only that it is working to conclude a deal “as soon as possible”, and hopes to do so during the autumn.
But Mr Raab told a cross-party committee of MPs that the end of negotiations, which have stretched on for 19 months, was now "firmly in sight".
The October summit of the European Council passed without a deal, and leaders of the remaining 27 EU countries decided not to schedule a special summit in November unless chief negotiator Michel Barnier told them there had been "decisive" progress in talks.
But Mr Raab appeared to suggest that he expected a deal within the next three weeks, as he set a date for himself and negotiator Olly Robbins to appear before the House of Commons Exiting the EU Committee.
"I would be happy to give evidence to the committee when a deal is finished and currently expect November 21 to be suitable," wrote Mr Raab.
The letter, released by the committee on Wednesday, was dated October 24.
'The end is firmly in sight'
Mr Raab wrote: "Despite our differences, we are not far from an agreement on this issue. We agree on the principle of a UK-wide customs backstop. An agreement on the details of that backstop should be possible.
"Both sides agree that this backstop cannot provide for a permanent UK/EU relationship and are committed to a future relationship that works for the whole of the UK, including Northern Ireland.
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"We are open to talking about ways to achieve this and committed to continuing discussions in order to reach an agreement.
"The end is now firmly in sight and, while obstacles remain, it cannot be beyond us to navigate them. We have resolved most of the issues and we are building up together what the future relationship should look like and making real progress.
"We now need to acknowledge the progress that has been made and now work rapidly through the remaining issues and come to an agreement that works for both sides."
Mr Raab had been due to give evidence to the committee on October 24, but pulled out shortly before the crunch October 17-18 European Council summit, with his office saying that he was committed to appear only once a deal was finalised.
In a letter accepting his proposal of a November 21 evidence session, committee chair Hilary Benn said he was "disappointed" with the new Brexit Secretary's failure to follow the pattern of regular updates established by his predecessor David Davis.
And he rejected as "not sufficient or effective" Mr Raab's proposal that he could update the committee by letter until the deal was agreed.
"Having been a member of this committee, you will know that this is not how committees undertake inquiries and is not conducive to scrutiny," said Mr Benn.