Labour MPs are being urged to back a plan to keep the UK in a Norway-style relationship with the EU, as MPs debate Brexit's next steps.
Axar.az reports citing BBC.
MPs will vote later to see if any proposals can win a majority - after failing to secure majorities last week.
Under the Common Market 2.0 proposal, the UK would leave the EU, but retain freedom of movement and make contributions to the EU Budget.
The Speaker has selected four motions, including one on a customs union.
International Trade Secretary Liam Fox told the BBC joining a customs union would be a "betrayal of Brexit".
The SNP are also proposing to back the Common Market 2.0 motion, put forward by Tory MP Nick Boles.
But the PM's spokesman said ending free movement was a "very important factor" for the public when voting for Brexit, so they would oppose it.
Shadow foreign secretary Emily Thornberry, speaking to the BBC's World at One programme, refused to say whether Labour's position on free movement had changed.
When asked if she was compromising on freedom of movement, she said "we are trying to pull the House of Commons together".
Conservative MPs are being given a free vote on the motions - meaning they will not be told by party bosses which way to go - but the cabinet has been told to abstain.
None of today's votes on the proposals are legally binding, meaning it will be up to the government if they act on the results.