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The FT reported that Lebedev met with Aidan Barclay, the chairman of the Telegraph Media Group, earlier this year and raised interest in buying the right-wing newspaper.
But Barclay, son of Sir David who owns the Telegraph Media Group with twin brother Sir Frederick, is said to have "made it very clear that the Telegraph was not for sale."
A spokesman for Lebedev, son of oligarch Alexander Lebedev, could not be reached for comment.
It is not the only bid for The Daily Telegraph the Barclay brothers have rebuffed this year, the FT added.
Former Daily Express and Newsweek editor-in-chief Richard Addis formed a consortium with the aim of taking The Daily Telegraph off the Barclay brothers' hands after they acquired it for £665 million ($867 million) in 2004.
He told the FT: "I created a small consortium interested in the Telegraph at the start of the year. We were active until April. There didn't appear to be any appetite to sell. If that changes we would regroup."
A Telegraph Media Group (TMG) spokesman is yet to respond to Business Insider's request for comment, but a representative of the Barclay brothers told the FT: "There are no plans to sell TMG or any part of it and there never have been."