Rogers was appointed to the role of permanent representative in 2013 by former prime minister David Cameron. He had been expected to play a key role in Brexit talks expected to start within months after Camerons successor at 10 Downing Street, Theresa May, triggers the exiting process in March.
Rogers was due to quit his job in Brussels towards the end of this year, but has decided to go earlier "after tensions with Downing Street," according to the FT report.
The Brussels-based Politico Europe in a brief report on Tuesday said that Rogers faced criticism after "a leak to the BBC revealed he had suggested it could take at least 10 years to agree a new trade deal with post-Brexit Britain."
The Foreign and Commonwealth Office in London said it would not comment at the moment on Rogers decision to quit, Xinhua reported.
Rogers, as Britains Permanent Representative to the EU, has overall responsibility for the work of the mission and represents the British government at weekly meetings of the Committee of Permanent Representatives in the Council of the EU. The committee deals largely with political, financial, justice, policing and foreign policy issues.