Former public relations executive Carter, who was recruited just 18 months ago, is due to release the - a strategy document to shape the communications industry including broadband for all UK homes, next week.
has reported he will announce his resignation on the eve of the report's launch.
Carter told the newspaper: "I'm beavering away feverishly on my report, that's my only preoccupation".
Carter initially served as the Prime Minister's chief of strategy and principal adviser. But, after a reported falling out with Gordon Brown's now-disgraced spin doctor Damian McBride, Carter became Communications Minister in October last year. He was tasked with the responsibility for reshaping internet and media regulation throughout Britain.
The Digital Britain report will propose measures to extend access to broadband internet services and revamp how public service broadcasting is funded. It will also tackle illegal downloads.