Russian businessman Lebedev was part of a consortium, including Mikhail Gorbachev, that last week agreed to buy the London paper from the Daily Mail and General Trust (DMGT).
However today, he tops a list of buyers rumoured to be in the running to buy ailing UK national The Independent and its titles.
In a statement to the London Stock Exchange, Independent News and Media (INM) announced that it was looking to offload any loss-making businesses, of which The Independent is one.
Despite there being no official announcement of a sale so far, a source close to INM told The Times: "Does Sir Anthony [Reilly, the major shareholder of INM] want to sell The Independent? No. Is it formally for sale? No. But is it fair to say he is open to discussions with potential buyers? Yes he is."
It is believed that Lebedev wants to become the UK's next Rupert Murdoch, and the 200,000-circulation Independent could be his next step towards achieving that.
Lebedev named as potential buyer for Independent
Following last week's confirmation that London's <i>Evening Standard</i> was to be sold to former KGB spy Alexander Lebedev, the rumour mill is now suggesting that the Russian billionaire is also in the running to buy national newspaper <i>The Independent</i> if it is put up for sale.