He said: "With no backstop, there will be no agreement".
"Dominic and I think it's possible to reach that agreement in October".
Mr Barnier was speaking following a six-hour round of face-to-face talks with the UK Brexit Secretary, Dominic Raab.
"It's as simple as that". Traders have become very concerned about negotiations in recent months, particularly the increased talk of no deal Brexit and these comments will at least start to alleviate those concerns.
Earlier, Mr Barnier said a backstop is "essential to conclude the negotiations", stating: "With no backstop there will be no agreement".
He said the issue was a matter of some urgency, and revealed he had asked Raab to provide data on how the necessary controls and checks take place.
Theresa May has repeatedly said she will refuse to contemplate any backstop deal that involves the "dislocation" of Northern Ireland from the rest of the UK.
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That goes specifically for the sensitive issue of the EU-U.K. land border between Ireland and British-ruled Northern Ireland, where the European Union wants a "backstop" solution in case of no deal, which includes terms that are anathema to London.
The UK Government insists that any backstop position should include the UK as a whole.
"The solutions (on Ireland) must be workable".
"We discussed a subject which is extremely important, serious, which is the security of our citizens", Barnier told reporters after the Raab meeting.
While this doesn't mean the EU's red lines have changed - in fact he explicitly confirmed that they must be respected, along with the UK's - it does suggest that more constructive conversations can happen to find a workable solution that suits both sides, should one exist.
Barnier emphasised again that the European Union and United Kingdom were working for an "unprecedented partnership" in the future that would include a free trade agreement, cooperation in areas of internal security, foreign policy, external security, and defence.
German foreign minister Maas adds "we are aiming for an ambitious and close relationship with Britian after Brexit both in economic and in security and foreign policy".