He also suggested that a transition period when the UK leaves "is not a given"
The EU's chief Brexit negotiator has warned that border checks with the North will be "unavoidable" if the UK leaves the single market and customs union.
The UK has already committed to avoiding any kind of hard border between Northern Ireland and the Republic after Brexit.
However, Michel Barnier gave a blunt assessment of the situation in Brussels earlier today.
He said: "It is important to tell the truth - a UK decision to leave the single market and to leave the customs union would make border checks unavoidable."
Speaking to reporters, Mr Barnier also warned that a transition period for the UK of around two years when it leaves the EU in March 2019 is "not a given".
He suggested there were still "problems" in Brussels with "understanding the position".
The EU is calling for freedom of movement to continue during the transition, but British officials want EU nationals who enter their UK during the transition period to be treated differently than those who entered before.
Earlier this week, Mrs May insisted the British government "will be robust in our arguments", while a government minister insisted the British Prime Minister "will stand up to anyone and everyone when it comes to maintaining the best interests of the UK".
Today, Mr Barnier indicated that the UK is looking for an agreement on a transition period by March.
He noted: "Our partners set out a certain number of disagreements which I regard as substantial.
"I'm surprised by these disagreements and if they persist, a transition is not a given."