A member of Labour's negotiating team, shadow business secretary Rebecca Long-Bailey said if no-deal became an option Labour would consider "very, very strongly" voting to cancel Brexit.
Long-Bailey suggested Labour could be prepared to cancel Brexit by revoking Article 50 - the legal mechanism through which Brexit is taking place - if the UK was heading towards a no-deal scenario on Friday.
"We have promised our party members and our constituents that we will do all we can to avoid a no-deal situation," BBC cited her as saying.
Long-Bailey also indicated more talks were likely to take place early this week.
At the same time, Andrea Leadsom, the Commons leader, said she would never agree to revoke article 50, and that no deal would be manageable.
The UK is scheduled to leave the EU on April 12, at 23:00 BST.
