Theresa May will meet European Commission president Jean-Claude Juncker next month as she steps up efforts to secure a breakthrough in the Brexit process.

The Prime Minister is under pressure from Brussels to spell out what she is prepared to pay in the so-called Brexit divorce bill, but Mr Juncker said he was “not crazy enough” to be drawn on whether an increased offer from Mrs May would be enough.

Mrs May is reported to be prepared to double her offer to around £38 billion in order to get the EU to agree to open crucial trade discussions in December.

It is believed no exact figure has been set, and the extra funding would only be on the table in exchange for fast-tracked talks on post-Brexit trade arrangements, and the framework for a two-year transitional deal after formal withdrawal in March 2019.

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Mrs May will meet Mr Juncker on December 4, 10 days before a European Council summit which could give the green light to trade talks.

At a press conference in Bern, Switzerland, Mr Juncker was asked whether the EU thought the increased offer from Mrs May was enough.

Jean-Claude Juncker speaks in Bern, SwitzerlandJean-Claude Juncker speaks in Bern, Switzerland (Peter Klaunzer/AP)

“I’m not crazy enough to give an immediate answer to your question,” Mr Juncker said.

“I will have a meeting with Theresa on December 4 and then all these things, proposals, will be submitted to our common meditation.”

The European Union’s chief negotiator Michel Barnier had suggested progress would be required by Friday, when Mrs May is set to take part in talks in Brussels.

READ MORE: Leaked Brexit paper gives damning verdict on UK Government's performance in talks

The European Commission said that Mr Juncker’s talks on December 4 were part of the “logical sequence” ahead of the December leaders’s summit.

A spokesman for the European Commission said: “This meeting should be seen as part and parcel of the logical sequence. Mr Barnier said we have got two weeks to make progress.”

Asked if there would be a seventh round of Brexit negotiations next week, the spokesman said: “It’s hardly a secret to tell you that we are all talking to each other at all levels.”

Speaking in German, Mr Juncker said that the EU and UK had got through the toughest parts of the first phase of negotiations, dealing with citizens’ rights, the Irish border and the financial settlement.

But he added: “I am not yet in a position to be able finally to say that sufficient progress has been made to move on to the second phase of negotiations, dealing with the future relationship.

“We will see about that in the next few days. I will meet Prime Minister Theresa May in Brussels on December 4, and then we will see whether we can move forward or whether we are stuck. My hope would be that we move forward.”

Mr Juncker added: “Brexit remains a tragedy. I am not happy at all about the fact that the British are leaving the European Union but it is a free, sovereign decision, which we have to respect. And our British colleagues have to respect that we also obviously have claims on Britain.

“The European Union is not leaving Britain, Britain is leaving the European Union.”