Brexit negotiator Michel Barnier warned last week the UK had just a fortnight to set out its position on a financial settlement with the EU.
Without that commitment, he claimed talks would not be able to move to the next phase and discuss future trade at next month’s EU summit.
It has been suggested Mrs May could ignore the deadline and make the UK’s final offer direct to EU leaders at the December summit.
Theresa May could be barred from making a final offer at the EU sumit by Angela Merkel
If she tries to do that, it will end in tears
But a Brussels diplomat told The Times Angela Merkel would never let that happen and only “fine-tuning” of the offer would be possible.
He warned any attempt to ignore the two-week deadline would result in a complete breakdown of talks.
He said: “If she tries to do that, it will end in tears.
“We know the British frustration but at this stage she does not have a choice.
Angela Merkel, Theresa May and Emmanuel Macron at the last EU summit
“Germany will not allow it. Full stop. It will be a breakdown.
“No one can afford that at this stage so we hope there is enough movement on the money and a commitment to avoid regulatory divergence between Northern Ireland and the Irish Republic.”
The Brussels broadside came as Theresa May met European business leaders at Downing Street and complained it was not clear what Brussels wanted from negotiations.
EU chiefs are adamant there must be clear progress on its three red line issues of the Brexit bill, Irish border and EU citizens’ rights.
Without it, talks cannot move on to the next phase, frustrating British efforts to start nailing down a trade deal before the UK leaves in March 2019.
Yesterday, David Davis announced MPs would be given a take it or leave it vote on any withdrawal agreement.
But he confirmed that, if the final bill was rejected, the UK would leave the EU without a deal.
The value of the apparent concession to rebels could be put to the test today as MPs resume debate on the Withdrawal Bill, also known as the repeal bill.
Crunch votes are not expected this week but there could be opportunities for MPs to signal their intent on key areas of disagreement, including a vote on the final deal and writing exit day into the legislation.