The two leaders will meet in Berlin on Friday ahead of a speech by the Prime Minister in Munich on Saturday on Britain’s future security relations with the EU.
But with talks opening last week on the second phase of the Brexit negotiations, she is facing demands from leaders of the remaining 27 member states to set out what sort of wider relationship she wants - including on trade.
On Wednesday a spokesman for Mrs Merkel said the British needed to come forward with concrete proposals, adding that “time is running out”.
It followed reports she had mocked Mrs May’s negotiating approach at last month’s World Economic Forum at Davos, complaining every time she asked her want she wanted, the Prime Minister replied: “Make me an offer.”
The latest German intervention echoed similar warnings from the EU’s chief negotiator Michel Barnier who said last week that a transition deal - which the Government is hoping to wrap up by the end March - was “not a given”.
He said there were “substantial” differences which had to be overcome if they were to agree transitional arrangements after the UK leaves in March 2019 to avoid the “cliff-edge” break which many businesses fear.
He also warned the return of border checks between Northern Ireland and the Republic was “unavoidable” if the UK pressed ahead with plans to leave the single market and the customs union - something ministers insist they do want to happen.
In setting out her negotiating aims, however, Mrs May has been constrained by the need to hold together her Government and her party which remain bitterly divided over what kind of post-Brexit arrangements they want.
In a keynote speech on Wednesday, Foreign Secretary Boris Johnson said Britain would be “mad” to accept a deal which did not allow it to capitalise on the full “economic freedoms” of leaving the EU.
While he insisted that the Brexit vote was not “some great V-sign from the cliffs of Dover”, he said the benefits the single market and the customs union were “nothing like as conspicuous or irrefutable as is sometimes claimed”.
His comments were in sharp contrast with Chancellor Philip Hammond - seen as the leading Cabinet proponent of a “soft” Brexit - who has suggested Britain’s relationship with the EU may change only “very modestly” after it leaves.
Many Tory Brexiteers remain angry at the EU’s insistence that the UK must remain subject to EU law - including any new legislation passed after it had left - during the transition period, expected to last around two years.
Feelings, which were already running high, were further inflamed when it emerged the EU was proposing a so-called “punishment clause”, which could see it impose sanctions on the UK if there is any breach of the rules.
But after Bexit Secretary David Davis accused the European Commission of failing to act in “good faith”, it was reported that officials from the other 27 states had agreed to tone down the language when they publish an expanded document towards the end of February.