The Independent board confirmed in December that it was negotiating with Lebedev who bought the Evening Standard title last year.
An initial deadline of 15 February was set for any purchase to go through, however, according to MediaWeek, this date will not be met. It quotes a source close to the deal, who has said the purchase is still a certainty to be completed.
Russian media magnate Lebedev came to prominence in late 2008 when he was touted as a potential buyer for the Evening Standard.
Since purchasing the title from DMGT he has upped its circulation to 600,000 and made it a free publication.
It is believed that he will do the same to the Independent.