Northern Ireland nationalists have said Stormont should not have a say over the Brexit backstop.
The British government is expected to table new proposals in a bid to break the border impasse but a role for the devolved assembly has been speculated.
Prime minister Theresa May's DUP supporters are adamantly opposed to any solution which would see any divergence between Northern Ireland and the rest of the UK.
Consulting Stormont on the backstop could effectively give the DUP a veto on a deal.
Pro-Remain parties including the SDLP and Sinn Féin met EU chief negotiator Michel Barnier on Friday.
The Green Party and Alliance Party were also represented.
During a post-meeting press conference, SDLP and Sinn Féin leaders Colum Eastwood and Michelle O'Neill told the BBC giving the suspended Stormont assembly in Belfast any say over the backstop would be unacceptable.
Mr Eastwood said: "The time to deliver on a deal is now. The North cannot be left to the fate of a reckless, no-deal Brexit."
The EU and UK have expressed hope a deal can be reached to avoid a hard Brexit.
Time is running out to secure an agreement and ratify it before the UK leaves in March.
Sammy Wilson, one of the DUP's 10 MPs at Westminster, said on Twitter: "If she is rolling back on her pledge that there will be no barriers between Northern Ireland and Great Britain, then the prime minister should be under no illusions; we will vote against her deal and it will go nowhere."
The EU and UK are at odds over the Irish border and the prime minister's Chequers plan is under attack from Brexiteers in her own party.
An EU leaders' summit is due in Brussels on October 17 and if a deal is close a special Brexit meeting could be called in November to sign off on it.
