Exploiting economic uncertainty officials will look to “shake the tree” and force firms to move their operations to the EU.
An EU source said: “The longer the UK waits, the more the pressure will build, the more we shake the tree.”
Brussels leaders are determined to force the Prime Minister into paying an eye-watering €60billion (£53billion) in order to secure a deal with the bloc.
European ambassadors gathered in Brussels to push Mrs May to commit to pouring the cash into the EU coffers and to discuss the next step in negotiations.
Talks will get underway again on Thursday with the ambassadors assessing what the proposed two-year transition deal might look like and outline their next move.
The source told the Telegraph: “The plain fact is that, as Mr Barnier repeatedly says, ‘the clock is ticking’, and time is not on the British side.”
It is understood that if no progress is made on the bill by December vital trade talks will be delayed until March as the stubborn bloc continues to move on to the next stage of talks.
An EU official said: “Some believe that the worse it gets for the British, the better for us… that maybe we could delay it all until, for instance, March, increasing the uncertainty and triggering the contingency plans in the corporate sector.”
In her Florence speech, Mrs May committed to paying €20billion (17.6billion) for a transition period and honouring existing commitments.
However, EU leaders were underwhelmed by the proposal demanding significantly more money.
Italy’s Europe minister, Sandro Gozi, said there remains “a lot to do on financial obligations”.
Trade minister Liam Fox blasted the EU and demanded they start making progress on Brexit following warnings from global business leaders that contingency plans are brewing.
The Secretary of State for International Trade took aim at the Brussels bloc for failing to move onto trade talks as Britain’s exit looms.
The Confederation of British Industry (CBI) warned on Monday that Brexit uncertainty could harm businesses.
But Mr Fox insisted a talk on trade in the House of Commons on Tuesday will ensure that businesses will not see a big change in their industries after Brexit.
Appearing on BBC News on Tuesday, Mr Fox said: “As you are well aware, the European Union are not yet willing to talk to us about that.
“That’s unfortunate because for a lot of businesses and a lot of international investors and a lot of European businesses – they want to know what that end state will look like so that they can plan now for that.
“And at this point, the British Government is urging the European Union to talk to about that so that we can get much better certainty and much better clarity on what the future relationships will look like.”
Several banks have started buying space in Germany’s financial hub of Frankfurt as some experts predict thousands of job loses in The City.
JP Morgan, Citigroup and Goldman Sachs have all signed deals or are closed to confirming new office space in Frankfurt.