Stanley Johnson, a former MEP who voted Remain in the referendum, has requested to become a French citizen as his mother Irene was born in Versailles.
The move was revealed by the prime minister's sister Rachel, an ardent Europhile, in her new book, Rake's Progress.
Ms Johnson said that her father is “en route to becoming a French citizen, as his mother had been born in Versailles and his grandmother had been in Paris”.
She added: “This is good news — I might be able to become French too.”
A source close to the family told The Sunday Times that Mr Johnson Sr has applied so that his grandchildren can live and work in the EU after Brexit.
Asked about obtaining a French passport last year, Mr Johnson said: “It’s a nice thought. These things are always among the options — members of my family might be [interested].”
The prime minister's family is famously split over Brexit, despite Mr Johnson's pivotal role in take the UK out of the EU.
His sister, Ms Johnson, joined the Liberal Democrats ahead of the 2017 election after denouncing Tory support for Brexit.
She defected to the short-lived Independent Group for Change last year, unsuccessfully standing as a candidate in the European elections.
Mr Johnson Sr, who was a Conservative MEP in the early 1980s, also campaigned for Remain during the referendum.
But his son, now the prime minister, was key figure in the Vote Leave campaign and won the 2019 election with a vow to "Get Brexit Done".
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