A member of Theresa May's cabinet has said the British government will have to 'consider very closely' any alternative Brexit plan backed by MPs.
In the wake of the House of Commons again rejecting Mrs May's withdrawal agreement on Friday, this week is expected to see further efforts to break the Brexit deadlock.
Tomorrow, the House of Commons is set to again vote on alternative proposals.
It will be the second batch of 'indicative votes' on possible options.
Eight possible alternative proposals were all rejected by MPs last week.
Two options - one relating to a customs union with the EU, and another for a 'confirmatory' public vote on any deal - gained most support.
Appearing on BBC's Andrew Marr Show, the UK's justice secretary David Gauke was asked what the government would do if MPs back an alternative such as a customs union.
He said: "We're clearly going to have to consider very carefully the will of parliament.
"My view is that the best outcome is the Prime Minister's deal... but if that is not the favoured outcome of parliament, then we would need to consider what parliament does want to do.
"If parliament moves in that direction... we would have to consider very closely what parliament decides to do."
Mr Gauke did indicate that Theresa May is unlikely to shift towards a no-deal approach, suggesting: "Parliament is not going to allow us to go down that route."
While there have been reports Mrs May is considering yet another vote on her deal, she continues to face strong opposition from the DUP and more than twenty Conservative Brexiteers.
Hardline pro-Brexit Tory Steve Baker today wrote in the Sunday Telegraph that the deal "cannot be allowed to go through at any cost".
The British government has less than two weeks to come forward with an alternative plan.
The Brexit process has already been extended until April 12th - or May 22nd if MPs do back the deal - with EU leaders to meet on April 10th to consider the situation.
Meanwhile, Labour's deputy leader Tom Watson has again called for a 'people's vote' on a Brexit deal.
He wrote in The Guardian: "Our plan to put any final Brexit deal back to the people has already begun to unite the Labour party.
"And, if the last referendum divided our country, I believe a new one might help heal it."