Mr Lebedev has already bought the Evening Standard in the UK
The company behind the Independent newspaper has extended talks with the Russian billionaire Alexander Lebedev.
Mr Lebedev has been in discussions with Independent News and Media (INM) over the ownership of its Independent and Independent on Sunday titles.
A deadline for talks was set for Monday, but the company has extended it to 26 February following delays.
It said it hoped the extension would "bring discussions to a successful conclusion".
Talks are reported to have been stalled by issues including printing contracts with rival media group Trinity Mirror, pensions deficits and redundancy costs.
Should it go ahead, the purchase of the Independent titles would mark Mr Lebedev's second move into the UK newspaper market.
Last year he bought the loss-making Evening Standard from Daily Mail & General Trust, turning it into a free newspaper.
Shareholders in INM are reported to be keen to get rid of the Independent titles, which are also loss making and suffering steady falls in circulation.