The decision behind the sale is so he can buy the NFL club Washington Commanders.
The Amazon billionaire is looking for a “clear way” to make the purchase by cashing in on the media outlet, according to the New York Post.
The report suggests that the Washington Post was bought by Bezos in 2013 for an estimated $250million [£202m].
The owner of the NFL franchise, Dan Snyder, has been tipped to be open to selling after the newspaper’s series of stories that alleged toxic management culture at the team.
The exposes also alleged that Snyder enabled sexual harassment.
The report says that there are some that believe that Synder suspects Bezos of encouraging the coverage in order to get him to sell the club.
While the billionaire says that there are no plans to sell the paper, a source told the New York Post: “I think Bezos’ people could go to Dan and say as a gesture of goodwill, ‘We are selling the paper.’
“I think that would go a long way with Dan.”
In December, there was reported to be a deadline for bids for the Commanders.
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But Bezos – who was believed to be in talks with rapper Jay-Z about a partnership – was not among the prospective buyers.
The Commanders are expected to be valued at between $5.5-6.5bn (£4.4-5.2bn).
Bezos has admitted that he is a fan of the sport as he revealed it was his “favourite sport” during an interview with CNN.
However, some sports journalists have insisted that Snyder is not keen on the idea of selling to the Amazon tycoon.
JP Finlay, who covers the Commanders for NBC Sports, tweeted: “Not only was I told Bezos didn’t submit a bid, I’ve had people tell me the Snyder family has absolutely no interest in selling to Bezos.”
While a source told NBC Sports’ Peter King: “It’ll never happen. Dan Snyder detests the Washington Post. No way he’d sell to the owner of that paper.”