Justice Secretary David Gauke has become the second cabinet minister to suggest Parliament could be given free votes on some Brexit issues.
He told the BBC MPs should be able to vote according to their personal views when the Brexit motion is debated on Tuesday, “to resolve things”.
He reiterated he would have to consider his position if the government opted for a no deal withdrawal from the EU.
Work and Pensions Secretary Amber Rudd has adopted a similar stance.
She told the BBC this week that she is “committed to making sure we avoid” a no deal Brexit and would not rule out resigning over it.
But 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 – who like Ms Rudd backed Remain in the referendum – warned that the way the UK leaves the EU should not be “railroaded through”.
The UK is due to leave the EU at 23:00 GMT on 29 March and the prime minister has faced repeated calls to rule out the prospect of leaving without a deal, if no agreement can be reached.
Theresa May is continuing to seek support for her Brexit deal, ahead of a crucial Commons vote on Tuesday. On 15 January, the withdrawal deal she negotiated with the EU was rejected by MPs by a historic margin – 432 votes to 202.
Opposition and backbench MPs have been tabling amendments to her motion in a bid to force the government to change direction.
On Friday, Commons Leader Andrea Leadsom said cabinet ministers should back the prime minister’s stance of leaving the option of a no deal on the table.
She also suggested the EU may be prepared to grant the UK a “couple of extra weeks” beyond the 29 March deadline to finalise preparations for Brexit.
However, Ms Leadsom said she had “grave concerns” about a bill, proposed by Labour MP Yvette Cooper, which could extend Article 50 – which triggers the UK’s withdrawal from the EU – by nine months.
Mr Gauke agreed with a suggestion that leaving without a deal could be “pretty disastrous” for the UK, saying it would have a “significant impact” on jobs.
He said: “What I have said repeatedly is if there is a conscious choice ‘right, that’s it, we’re going no deal’ when there are other options available, that would be something I would find extremely difficult.”
Asked whether he backed MPs being given a free vote on extending Article 50, Mr Gauke 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.
“I do think that Parliament is entitled to be involved in this process.”