IN&M today announced to the stock exchange that "the period of exclusivity has been extended from today to 26 February to facilitate bringing these discussions to a successful conclusion".
Lebedev, who owns a majority stake in London's flagship daily newspaper, The London Evening Standard, first entered into negotiations with IN&M in December last year.
Media Week had previously reported that the initial month-long deadline for exclusive negotiations, due to end today, would be extended as the two parties thrash out final contract details.
One sticking point hampering negotiations is thought to be resolving printing contract issues and the transfer of staff. IN&M currently holds a long-running printing contract with Trinity Mirror.
Lebedev is thought to want to switch printing the papers to The Daily Mail's presses, which currently print the London Evening Standard.
Should Lebedev complete the purchase of the two titles it would put him in the unique position of owning a national morning newspaper and an afternoon free title.
Sources suggest that IN&M is likely to receive a nominal sum for the two newspapers, which have both been losing circulation. The Independent's January circulation was down 13.8% year on year and The IoS down 13.9%.
INM will report its financial results on 24 March.
Lebedev declined to comment.