Justice Secretary David Gauke has become the second cabinet minister to suggest Parliament could be given free votes on some Brexit-related issues.
Gauke is the second MP to speak as Work and Pensions Secretary Amber Rudd has adopted a similar stance earlier this week.
She said allowing a free vote could help establish what Brexit solution could command a majority among MPs.
Speaking on BBC Radio 4’s Any Questions, Mr Gauke said MPs should be given free votes, even if it potentially led to an extension of Article 50.
He said: “I think there is a case for free votes in this area to resolve things.
“As far as Tuesday is concerned… we need to see what all the amendments are going to be, to see whether Tuesday is a crunch point or not.”
On Tuesday, January 29, the House of Commons will see MPs vote on Theresa May’s next steps for Brexit.
Mr Gauke also agreed with a suggestion that leaving without a deal could be disastrous for the UK, saying it would have a “significant impact” on jobs.
He said: “If there is a conscious choice, ‘Right, that’s it, we’re going no deal’, that would be something I would find extremely difficult.”