The reports have triggered speculation that Carter may be in line to take the chief executive role at ITV.
The ailing broadcaster has been searching for a chief executive to turn its fortunes around since Michael Grade announced he would be stepping down from the post.
The government has not confirmed Carter's departure but the minister himself has not denied the reports.
The Digital Britain report will set out guidelines for the government to shape the future of the UK's communications industries. It will have a huge impact on broadcasters, which are struggling against falling ad revenues and failing to monetise digital opportunities effectively.
Carter is a former chief executive of City PR firm Brunswick and of regulator Ofcom.
He became communications minister last October after 10 months as the prime minister's chief of strategy and principal adviser.
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