The compromise motion, also known as Norway plus, is the brainchild of Tory MP Nick Boles and takes as its starting point the Scandinavian country’s relationship with the EU.
The move came as Ian Blackord, the SNP leader at Westminster, insisted that revoking Article 50 or holding a second EU referendum must now be the priorities for Parliament.
“After three resounding defeats, Theresa May must finally accept her damaging deal is dead - and stop acting as a roadblock to progress,” the MP said.
“Parliament must move, either to revoke Article 50 and put a stop to this process or to call a fresh referendum, with the option to Remain.”
Boles’ plan was defeated by 283 votes to 188 when it was first put to the House on Wednesday as one of eight indicative votes, with the 35 SNP MPs abstaining.
Nationalists have faced criticism for failing to support other soft Brexit alternatives to Theresa May’s deal, which was voted down for a third time on Friday.
But the party is now weighing up whether the Boles amendment offers the best chance of avoiding a no deal Brexit.
Last night, Stephen Gethins, the party’s foreign affairs spokesman, said: “The SNP’s priority is to remain in the EU and that is why we will be voting for amendments to revoke article 50 and to give the people a final say.
“We recognise that the proposal from Nick Boles, has some similarities to the compromise position set out by the Scottish Government, and support it being debated again next week.
“The SNP will continue discussions with other parties over the weekend, however our preference remains stopping Brexit and keeping Scotland in the EU.”
Nicola Sturgeon said the party would decide how to vote when it saw what options were available, but indicated it was unlikely her MPs would back a customs union amendment which was also voted down last week.
She added: “A customs union on its own is not a position we’ve advocated because it would not protect Scotland’s interests.
“The compromise we proposed - only if remain not an option - was full single market and customs union membership.”
Edinburgh South West MP Joanna Cherry will also table a revised version of her amendment on Monday which calls for Article 50 to be revoked.
The SNP’s justice spokeswoman said she had “worked cross-party to get a bigger consensus”.