"The EU is like the Hotel California - we will never leave", he said.
The UK government concedes, however, that to uphold its commitments with regard to the Irish border "an approach on regulatory standards ... will also need to be addressed".
The Good Friday Agreement has regulated on the border issues, but some of May's proposals put that in threat.
"We look forward to the passage of the EU Withdrawal Bill next week and hope that, whether various amendments are passed or defeated, we will have a clearer picture of what happens next".
Even if he hadn't, the government's proposed backstop would have set us on the road to Remain by another name. "Time is running out", Barnier said.
At the heart of the problem is ensuring there is no hard border between Northern Ireland and the Irish Republic, which both Britain and the European Union have committed to.
And amid the torturous, anorakish Brexit debate, replete with talk of backstops, a customs union, the Customs Union, a customs partnership, max fac, regulatory alignment, regulatory divergence, cherry-picking and cake-eating, it is a question that we can not let escape us. The current proposal would see Britain applying the EU's external tariffs for a limited period beyond December 2020. But it also risks causing more domestic trouble for May, who needs to keep her divided Cabinet together and the Northern Irish party that props up her government onside.
"I've always been clear that this was time-limited and as we've said today [Thursday] the end state at the latest will be in by the end of 2021 and we will be working to ensure that it is in earlier than that". "In less than 10 months the United Kingdom is leaving the European Union as it has wanted", Barnier said.
Claiming there is "clearly a great deal of work" remaining to be done in Brexit negotiations, Mr Coveney said: "Our strong preference remains an overall EU-UK future relationship which would resolve all issues".
But he said: "Theresa May and her team have agreed to the backstop in the March agreement and there is no question of backtracking on that".
The Government did not expect it to be implemented, as it meant to have a permanent customs arrangement in place by the end of 2020, she said.
One of the options now being considered is to keep Northern Ireland - not mainland Britain - aligned with those rules, according to the person.
It was not clear whether the European Union would accept the proposal.
Liberal Democrat leader Sir Vince Cable, Tory former minister Anna Soubry and Labour's Chuka Umunna denounced as a "profound mistake" Brexiteers' claims that new deals with countries like the USA and China will make up for trade lost due to withdrawal from the EU.
In the 2016 referendum, Northern Ireland voted 56 percent to remain in the European Union but, like Scotland, was outvoted by England and Wales and the overall result was 52 percent for Brexit.