Mr Lebedev bought the Evening Standard earlier this year
The owner of the Independent and the Independent on Sunday has said it is in exclusive talks to sell the titles to the owner of the Evening Standard.
Alexander Lebedev has held talks over the past year with Independent News & Media to buy its national newspapers.
The Russian businessman bought the Evening Standard, which is now given away free, earlier this year.
Many newspapers are struggling with falling circulations as readers move increasingly to online content.
They have also suffered during the recession from falling advertising revenues.
Independent News & Media (INM) said that talks with Mr Levedev were still at an early stage and were subject to due diligence and several contractual conditions.
"As such, there is no certainty that these discussions will lead to the finalisation of a transaction of any kind," it said.
The exclusivity agreement with Mr Lebedev runs until 15 February.
The Independent already shares the same offices as the Evening Standard.
INM has been struggling to repay debts but has now come to an agreement with creditors, allowing the on-off talks to resume, reports suggest.
The group reported pre-tax loss of 161m euros (£144m at the time) last year, down from profits of 248m euros in 2007.