Mr Barnier said this week's fifth round of negotiations ended without making any "great steps forward" and there was "deadlock" on the UK's financial settlement.
He told a press conference in Brussels at the conclusion of the four-day talks: "On this basis I am not able in the current circumstances to propose next week to the European Council that we should start discussions on the future relationship."
Mr Barnier's comments represent a setback to the UK Government, which had been hoping to persuade the remaining 27 EU leaders at the October 19 summit that sufficient progress had been made on the divorce deal to move on to discussions on the future UK/EU relationship on issues including trade.
Mr Barnier told a closing news conference in Brussels the talks had "clarified" some issues but that more needed to be done.
And he said there was "deadlock" on the issue of the scale of Britain's financial settlement, a subject on which there were no negotiations this week.
Mrs May's announcement in her Florence speech that Britain would honour commitments entered into as an EU member was important, he said.
But he added: "This week, however, the UK repeated that it was still not ready to spell out these commitments.
"There have therefore been no negotiations on this subject. We confined ourselves to technical discussions - useful discussions, but technical discussions.
"On this question we have reached a state of deadlock which is very disturbing for thousands of project promoters in Europe and it's disturbing also for taxpayers."
Mr Barnier held out the hope for progress by the time of the December summit of the European Council.
But he insisted the EU would not make "concessions" on the three key withdrawal issues of expats' rights, the status of the Irish border and the UK's financial contribution.
He said it was vital that the final relationship between the UK and the EU was based on "confidence", adding: "Confidence must follow from clarity and the honouring of all commitments we have entered into together as the 28."
Mr Barnier said: "We are not asking the British to make concessions. The agreement we are working on will not be built on concessions.
"There is no question of making concessions on citizens' rights. There is no question of making concessions on the peace process in Northern Ireland.
"As regards the financial settlement, there is no question of making concessions on thousands of European investment projects throughout Europe."
He added: "We have shared objectives and we have shared obligations. We also have shared duties and we shall succeed only with shared solutions. That is our responsibility.
"I've been saying since the Florence speech that there is a new momentum, and I remain convinced today that with political will, decisive progress is within our grasp in the next two months."
Mr Barnier said negotiations on the status of the Irish border had "advanced" during this week's discussions.
But he said there was "more work to do in order to build a full picture of the challenges to North-South co-operation resulting from the UK - and therefore Northern Ireland - leaving the EU legal framework".