Britain is due to leave the EU by the end of March 2019, after a June 23 referendum last year in which many Britons backed Brexit to restrict immigration and regain powers from Brussels.
Some senior members of Prime Minister Theresa May's cabinet, including finance minister Philip Hammond, have been pushing for a transitional period designed to protect the economy and reassure businesses.
As part of Hammond's plans, EU citizens would still be able to move to Britain for up to two years, The Times newspaper reported on Friday. The Guardian newspaper cited a senior cabinet source as saying free movement could last for up to four years.
A spokeswoman at May's office did not offer an immediate comment when contacted by Reuters on Friday.
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