The UK has been urged to table fresh proposals within the next 48 hours to break the Brexit impasse.
EU officials said they would work non-stop over the weekend if "acceptable" ideas were received by Friday to break the deadlock over the Irish backstop.
The UK has said "reasonable" proposals to satisfy MPs' concerns about being tied to EU rules had already been made.
It comes as Jeremy Corbyn has met Conservative MPs to discuss possible alternatives to the PM's deal.
The Labour leader held talks with ex-Tory minister Nick Boles and Sir Oliver Letwin, who favour a closer, Norway-style relationship with the EU.
He said he had discussed the so-called "Common Market 2.0 option" - which would see the UK remain in the EU's single market by staying part of the European Economic Area - but would not commit to backing it at this stage.
No breakthrough in Brexit talks, says EU
Brexit: A really simple guide
There have been few visible signs of progress ahead of Parliament's second vote on the Brexit deal next Tuesday.
MPs emphatically rejected the terms of withdrawal negotiated by Theresa May in January.
If they do so again, they will get to choose between leaving without a deal or deferring the UK's exit from the EU beyond the scheduled date of 29 March.
The PM is seeking legally-enforceable changes to the backstop - an insurance policy designed to prevent physical checks on the border between Northern Ireland and the Republic of Ireland.