Angela Merkel said she wanted to see the UK stay in the EU and, suggesting co-operation between the two countries, added that she hoped the British people would decide to remain "in a way that would make us stronger in Europe".
Her comments came ahead of a speech by George Osborne in which he set out five of the UK's key economic demands in its renegotiation talks with the EU.
Addressing a conference of business leaders in Berlin, Mr Osborne said EU arrangements "are not suitable for countries that aren't in the euro" and demanded that British taxpayers never bear the cost of bailing out the eurozone.
And he proposed the two countries work together to get Britain what it wanted.
He said: "So let me be candid: there is a deal to be done and we can work together."
Mrs Merkel appeared receptive to the Chancellor's approaches and told the conference: "For us, it is important for many reasons to keep Great Britain as a member of the European Union.
"That is why we will do what we can so that Britain can stay.
"The rest is up to Britons to decide. I do hope they do it in a way which will make us stronger in Europe."
Mr Osborne - who is taking a lead role in negotiations ahead of an EU referendum before the end of 2017 - argued that further integration was putting a "strain" on Britain's relationship with Europe.
He outlined five key demands, or safeguards, for the Government as it seeks to change Britain's relationship with the EU before the in/out vote.
:: Support for the integrity of the European Single Market
:: EU institutions must recognise that the EU has more than one currency
:: Non-eurozone members of the EU must be protected if the union integrates further
:: Participation in the banking union must be voluntary
:: UK taxpayers must not be responsible for bailing out eurozone countries
Critics pointed out the points were already recognised in Britain's relationship with the European Union and Mr Osborne was arguing for powers it already had.
Last month David Cameron came under pressure from European leaders to set out his demands in renegotiation talks and he said he would do so in early November.
The Prime Minister will be held to close account on any demands he sets out by eurosceptic Conservative MPs and Brexit campaigners.
Speaking to business leaders in Berlin, Mr Osborne said: "Quite frankly, the British people do not want to be part of an ever closer union.
"We want Britain to remain in a reformed European Union, but it needs to be a European Union that works better for all the citizens of Europe - and works better for Britain too.
"It needs to be a Europe where we are not part of that ever closer union you are more comfortable with.
"In the UK, where this is widely interpreted as a commitment to ever-closer political integration, that concept is now supported by a tiny proportion of voters.
"I believe it is this that is the cause of some of the strains between Britain and our European partners.
"Ever closer union is not right for us any longer."
Shadow chancellor John McDonnell said: "This trip is a meaningless publicity stunt as he is demanding powers of veto that we already have.
"These conditions are all straw men that the Chancellor wants to then knock down and claim victory to a home audience."