Mr Cameron has said the UK will use the opportunity of further integration in the eurozone to recast Britain's relationship with Brussels. Several Cabinet ministers, led by Education Secretary Michael Gove, want to threaten to withdraw from the EU altogether to get a better deal. However, senior sources in Berlin say Mrs Merkel - who is due to visit London early next month - is ready to cut the UK adrift.
Der Speigel, which boasts close links to the upper echelons of the German government, described a Europe in which the British are at best spectators in the gallery, like Statler and Waldorf, the two old men on The Muppet Show.
Sources in Berlin said the report reflects the views of the Merkel government, and is likely to have followed a briefing by aides of the Chancellor.
The magazine reported that Mrs Merkel was previously keen to reflect British sensibilities, as the UK is a useful counterweight to France in Europe, but she has now tired of complaints about the direction of the EU. She had repeatedly said privately that one should not give the British the feeling that they are no longer part of Europe, and that the door must be kept open for London, the magazine said.
But the Cameron administrations unwillingness to compromise leaves the German government with no choice.
In reality the Chancellor has long since come to terms with the fact that there will no longer be a path back to the centre of the union for the British.
Herbert Reul, the chairman of the group representing Mrs Merkel's centre-right Christian Democratic Union in the European Parliament, said: The British are increasingly perceived as a divisive force. Hardly a day goes by on which they do not raise new demands.
The sentiment they should just leave has become common among my colleagues.
Mr Cameron and Mrs Merkel spoke by telephone yesterday ahead of a summit in Brussels this Thursday. The pair are expected to clash over plans for a European banking union, which Downing Street fears will undermine the City of London.