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Business Insider hears that Johnson was consoled by a top BBC executive after he ruled himself out of the race to replace former prime minister David Cameron.
During the exchange, the bombastic Tory MP contemplated a change of career. Johnson is alleged to have texted his BBC friend: "If you're looking for the new face of 'Top Gear,' I'm your man."
A source said the idea was not entirely dismissed by the broadcaster. "It's one of the things that's a joke, then you think: Hang on, this might be the exact answer to all the BBC's problems," they laughed.
It is not the first time that Johnson, now foreign secretary in Theresa May's government, has thrown his hat in the ring for a job on "Top Gear."
When Jeremy Clarkson was sacked by the BBC last year, Johnson was asked during a Twitter Q&A if he fancied replacing the presenter. "Am mega Clarkson fan but if a vacancy wd def [sic] let my name go forward," he tweeted.
Johnson is no stranger to the show. He was the "star in a reasonably priced car" in 2008, completing his lap in 1 minute 56 seconds.
The Brexiteer also wrote a motoring column for GQ and was described by website Car Keys as "the world's worst car journalist." In a missive about the Ferrari F430, Johnson once wrote: "It was as though the whole county of Hampshire was lying back and opening her well-bred legs to be ravished by the Italian stallion."