Cummings, who is a non-elected aide to prime minister Boris Johnson, travelled 260 miles from his London home to Durham in April, with his wife, Mary Wakefield, who was exhibiting symptoms of coronavirus, and his children.
He also was caught making a 30-mile trip to Barnard Castle on Wakefield's birthday, which he claimed was intended to test out his eyesight after suffering vision problems as a result of Covid-19.
Piers Wenger, the controller of BBC drama commissioning, was asked by The Radio Times whether the broadcaster would consider purchasing the rights to a drama adaptation.
"In the right hands, yes," he responded.
He also said that the BBC had already received pitches from writers who were keen to adapt the story.
Cummings has been portrayed on-screen before, by Benedict Cumberbatch in the Channel 4 miniseries Brexit: The Uncivil War.
His contravention of quarantine rules dominated headlines for days as people from across the political spectrum called for his resignation.
While it could be some time before his story gets adapted into a drama, the infamous drive to Barnard Castle has already been replicated in a satirical video game, called 30 Miles to Barnard Castle.
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