"I would be happy to give evidence to the committee when a deal is finalised, and currently expect 21 November to be suitable," he wrote.
Both Raab and Oliver Robbins, Prime Minister Theresa May's chief Brexit advisor, have been invited to address the committee on that date.
Most of the divorce deal with Brussels is agreed but talks remain stuck on how to avoid new checks on Britain's land border with EU member Ireland after it leaves the bloc's single market and customs union.
Raab will visit the UK province of Northern Ireland on Friday on a "fact-finding trip", which will include meetings with local businesses and politicians, an official in his ministry told AFP.
EU leaders had mooted a special summit in mid-November to seal the Brexit deal, but warned earlier this month that this would not happen without more progress on the Irish issue.
Raab wrote: "The end is now firmly in sight and, while obstacles remain, it cannot be beyond us to navigate them." However, May's spokesman refused to repeat the date of November 21, only repeating that "we wish to conclude the deal as quickly as possible".
Previously, he had said the government was pressing for a deal this autumn.
British officials are keen to avoid the negotiations dragging on, with Brexit day scheduled for March 29.
Separately, Raab's predecessor David Davis, who quit over the government's approach to Brexit in July, said the final deal will likely pass when it comes to a vote in the House of Commons.
Davis is among a large minority of May's Conservative MPs who strongly oppose her strategy, raising fears the deal will be rejected.
"The fear of no deal, I think.... that will win and there will be a deal," Davis told an event on Tuesday evening, according to Sky News television.
Davis on Wednesday retracted his reported remarks saying that any deal similar to May's current plan of close economic ties with the EU "will not pass the Commons". (AFP)
(This story has not been edited by Devdiscourse staff and is auto-generated from a syndicated feed.)