By Paul Carrel

BERLIN (Reuters) - German Chancellor Angela Merkel signaled a readiness on Tuesday to discuss the parameters of the free movement of people in the European Union, suggesting there may be some room for maneuver on the issue in talks on Britain's exit from the bloc.

Merkel said the EU could not divide its four freedoms - of 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 close to 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 major issue for many of the 52 percent of Britons 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 Germany's BDA employers association.

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 life-long 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," she said.

The nuance around when to apply the principle of free movement of people could prove welcome to British Prime Minister 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 newspaper 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.

May has promised to trigger divorce proceedings with the EU 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 set package of principles rather than an à la carte 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 criticized 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.

(Editing by Hugh Lawson)