He qualified that by saying that he was "not actively trying to sell it".
Mr Lebedev also owns the London Evening Standard and the Independent's sister newspaper, i.
On Monday he launches London Live, a 24-hour television network dedicated to news, entertainment and culture in the capital.
On The Andrew Marr Show Mr Lebedev said he hoped the TV channel would create jobs and be a platform to launch new talent.
He has hired what he described as "YouTube sensations" and relative unknowns to present its programming.
Another innovation Mr Lebedev highlighted was the broadcast of live plays.
Asked about his newspaper business, Mr Lebedev underlined the re-invigoration of the London Evening Standard under his ownership, which - since becoming a free title - has gone from a circulation of 700,000 to 900,000.
From losing Â£30m a year, the Evening Standard now makes a profit.
He also said the Independent and the i newspaper were together losing Â£5m-a-year, compared with a Â£20m loss in the previous year.
Those two newspapers have long been rumoured to be for sale. The latest comments from Mr Lebedev are a sign from the owner that he is entertaining offers.
Mr Lebedev, 33, is a British citizen and told Andrew Marr he had been a Londoner since the age of eight. He also owns a pub, the Bunch of Grapes, in East London.
He still owns several properties in Crimea.
Asked if he was worried about them in the light of the Russian incursion, he said he was "very concerned", but the situation there was "complicated and textured" and a lot of the time was misunderstood in the West.
London Live goes on air at 18:30 BST on Monday on channel 8 on the Freeview service.
The owner of the Independent, Evgeny Lebedev, says the newspaper could be for sale if somebody "offers the right price".