Now it has been confirmed that European Council president Donald Tusk will formally propose a new timetable at the EU leaders summit being held in Salzburg on Wednesday and Thursday.
His comments came as the Prime Minister prepares to head off to Salzburg later today for an informal summit with fellow European Union leaders when, tomorrow over dinner, she will argue for her Chequers Plan, stressing how she needs Brussels to move to help her get her proposal through Westminster.
A spokesman for the Home Office said: "After we leave the European Union, we will take back control of our borders and put in place an immigration system that works in the interests of the whole of the UK".
He stressed that the EU needed to protect its single market from Britain piggybacking on Northern Ireland's special status and to provide a "legally operational" solution - meaning he will resist a political fudge in language or a deal that would push resolution of the Irish problem until after Brexit in March and into negotiations on a future EU-UK trade agreement.
British Prime Minister Theresa May on Monday gave the first major indication that immigration rules for non-EU citizens such as Indians are set to be closely aligned with those for European Union nationals once Britain has left the economic bloc by next year.
"It's then that we shall see whether the agreement we are hoping for is within our grasp", Mr Barnier said.
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Speaking about Brexit, he told the Associated Press: "I don't think it's brinkmanship".
The long-awaited report also recommended that the United Kingdom make it easier for high-skilled workers to migrate to Britain, advising that it ditch the cap which now stands at 20,700 each year for people from outside Europe.More news: Why getting one of the new iPhones might not be worth it
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The EU is standing by its demand for a legal backstop in any deal precluding a "hard border" Ireland that would undermine the Good Friday peace accord.
However Mrs May has rejected the plan as unacceptable, arguing that it would effectively create a border in the Irish Sea between Northern Ireland and Great Britain.
Mr Barnier said he was working on a plan to "de-dramatise" the controls that would be necessary in the event of the backstop coming into play.
"So that frictionless movement is at the heart of the new proposals we put forward this summer", she added.
"For industrial goods there is this well known [trusted trader] system where you don't have to have checks at the border as such", says one member state official who was present, "where you can carry out checks at the place of destination by market surveillance authorities, where the risk is low".
"The pressures this causes means that we have to turn away qualified doctors, teachers, and entrepreneurs from non-EU countries who would make a positive contribution to this country".
"Unfortunately, a no deal scenario is still quite possible.
I think words have helped, they've changed the atmosphere, but we need to see actions now", he said. Still, Tusk believes that in the weeks ahead "if we all act responsibly, we can avoid a catastrophe" of Britain crashing out without a deal.