The German chancellor, Angela Merkel, has signalled a readiness to discuss the parameters of the free movement of people in the EU, suggesting there may be some room for manoeuvre on the issue in Brexit talks.

Merkel said the EU could not divide its four freedoms – movement of goods, capital, people and services – to allow Britain to restrict immigration from the bloc while retaining tariff-free access to the market of almost 500 million people.

But she opened a door to discussions on the framework of the free movement of people, in a potentially significant development for Britain, where controlling immigration was a big issue for many of the 52% of voters who backed leaving the EU.

“Were we to make an exception for the free movement of people with Britain, this would mean we would endanger principles of the whole internal market in the European Union, because everyone else will then want these exceptions,” Merkel told a meeting of the German employers’ association BDA.

But on the finer detail of defining the free movement of people, she added: “I personally am of the view that we will have to discuss further with the [European] commission when this freedom of movement applies from.”

Merkel said that if, for example, someone came to Germany from eastern Europe and worked only for a short time but acquired a lifelong claim on welfare benefits, “then I see a question about which we must talk again. Free movement applies to me in the sense that the employee himself earns the money he needs for himself and his family in the other member state.”

The nuance on when to apply the principle of free movement of people could prove welcome to Theresa May, who has said Britain does not face a “binary choice” between curbing immigration and getting a good trade agreement.

Offering “fair” negotiations, Merkel added: “First, however, Britain must explain in what manner it would like this exit.”

A memo written for May’s government and leaked to the Times said that Britain has no overall Brexit strategy and that splits in the cabinet could prevent it from agreeing on a clear negotiating position for six months. The prime minister has promised to trigger article 50 by the end of March.

So far the bloc has portrayed the single market, which Britain may subsequently try to retain membership of, as a package of principles rather than a menu that Britain can pick and choose from. Merkel reiterated that broad principle, telling the BDA: “In my firm view, we cannot wobble on the basic principle of free movement of people.”

The chancellor said it was paradoxical that Britain had criticised Germany and other EU states for using so-called transitional arrangements to temporarily restrict the free movement of workers from eastern European countries that joined the EU in 2004 and 2007, but now wanted to restrict movement across the bloc. “That is not on,” she said.