David Cameron won an early boost in his drive to win a new deal for Britain in the European Union when Angela Merkel said it could consider amending its treaties as the price for persuading Britain not to leave.
Mr Cameron has argued that treaty change is essential to impose new limits on the entitlement of EU nationals to receive benefits in Britain.
He has run into early opposition in France and Poland, but the German Chancellor said she was confident a deal could be struck to enable Britain to remain in the bloc.
“I’m optimistic that if we all want it, we’ll find a good solution,” she told the BBC.
“It’s not about losing sleep over this, but about doing our work and creating the necessary preconditions for Britain to remain.”
Ms Merkel, whose backing is crucial to Mr Cameron’s hopes of renegotiating Britain’s relations with Brussels, said history showed the EU could successfully address member states’ concerns.
Her words of encouragement came after a former German foreign minister, Joschka Fischer, warned Britain against “wishful thinking” over the level of support it from Berlin.
He said: “Angela Merkel will do nothing which will endanger the basic principles of the common market, of the EU.”
The Prime Minister’s official spokeswoman said Mr Cameron was prepared to hear lots of different views during the renegotiation.
“What matters is he is setting out very clearly why he wants to address the concerns of the British people and how he wants to progress with that ahead of the referendum. Those discussions have begun in a positive and constructive spirit,” she said.