David Cameron is to discuss European reform with the German chancellor, Angela Merkel, on a visit to Germany on Friday.

In a highly unusual move, Merkel has invited the prime minister and his family to stay at her residence in Meseberg, outside Berlin – the German equivalent of the prime minister's country residence, Chequers.

It is the first time Cameron's wife, Samantha, and their three children have accompanied him on an official visit. Also unusually, Merkel's husband, Joachim Sauer, will be present at the gathering.

The two leaders will talk over "all aspects" of European reform as well as the forthcoming G8 summit and the situation in Syria, the a spokesman for the prime minister said.

Germany has reacted coolly to Cameron's calls for a renegotiation of Britain's relationship with the EU. He was dealt a major blow this month when Merkel and the French president, François Hollande, snubbed a UK exercise to assess the impact of EU laws and regulations on Britain and the rest of Europe. The "balance of competences" review was dubbed a questionnaire by Berlin and Paris.

Merkel has made no secret of her concerns about Cameron's plans to renegotiate Britain's relationship with the EU before staging a referendum on its continuing membership. But the personal nature of the arrangements for the Meseberg visit suggest Merkel may be seeking to build bridges with Cameron and keep him onside during such a difficult time for the eurozone.

Earlier this week Cameron said British voters' support for EU membership was "wafer-thin". In joint interviews with five European newspapers, he said the EU "sometimes overreached itself with directives and interventions and interference", and stressed the need for a more flexible Europe.

But he also insisted he was not demanding change simply for the sake of Britain. Reform was in the interests of the EU as a whole, he said.

"What I want to do is achieve a reform of the European Union," he said. "We're in a global race where we have to compete with [countries such as] India, China, Indonesia and Malaysia. We need a Europe that is more open, that is more competitive, that is more flexible, that thinks more about the cost that it's putting on businesses, particularly small businesses. We want a world that wakes up to this modern world of competition and flexibility. That is the aim."

Cameron also said in his interview he was convinced there would be a need for treaty change in the EU in the future, even though the French and the Germans have expressed their opposition to a full overhaul of the laws governing the EU.

In his Bloomberg speech in January, Cameron committed himself to changing Britain's relationship with the EU and then holding an in/out referendum by the end of 2017 at the latest. Without a full treaty renegotiation, he might find it hard to secure significant reforms.

On Friday, Michael Meister, deputy parliamentary chairman of Merkel's Christian Democratic Union party, said Germany was "open for arguments" about moving some powers back into the hands of member states.

"We want to unify Europe and we have to do it together, and I think there are a lot of common ideas with the British side and the German side on it," he told BBC Radio 4's Today programme.

"It's a good thing that we have an idea of a private competitive economy and that's much different from other countries in Europe."

Meister said he recognised the need for compromises. "I think we are open for arguments why it makes sense and follows the principle of subsidiarity to move something back [to member state control]," he said.

"But then you need good arguments … to show there is no reason to move it on a common level. We are now 27 [member states], and maybe from the middle of the year 28 countries, and I think we need compromises which develop the EU in the future because all the single nations are not powerful enough to stay in a global competition."

Andrea Leadsom, Conservative MP for South Northamptonshire and a member of the Fresh Start Group, which wants to renegotiate Britain's relationship with the EU, also said she accepted the need for compromise.

"I don't think anybody on the backbenches or the frontbenches of any party thinks laying down the law is at all possible or plausible or desirable," she told the Today programme. "So, compromise is of course the way you do anything.

"The Foreign Office have not traditionally been incredibly brave or ambitious in negotiations and we certainly need to be braver in sticking to our corner. I think David Cameron has been and will continue to be, so I think we are in a very good place."

No 10 said it was trying to reschedule a meeting with Hollande after Cameron pulled out of talks in Paris on Monday after the death of Lady Thatcher.