The Foxes have been linked with a move for the French midfielder in the coming months, with Youri Tielemans expected to leave the King Power Stadium this summer following their failure to qualify for continental football.
Brendan Rodgers is therefore keen to fill the gap expected to be left behind by the departing Belgian, and Aouar could cost as little as £13m according to RMC Sport.
With the 23-year-old entering the final year of his deal with the Ligue 1 side this summer, Lyon are reportedly willing to part ways with the central midfielder to avoid losing him on a free transfer in 12 months time.
Arsenal had previously been heavily linked with a move for Aouar in the past, but no move materialised to bring him to the Premier League.
However, the report does suggest that Monaco, Real Betis and Marseille also hold an interest in acquiring Aouar's services in the coming months, but Rodgers will be hopeful that the lure of Premier League football could help them land their target.
Following his breakthrough season with Lyon in 2016-17, Aouar has gone on to make 214 appearances for them across all competitions, scoring 39 goals.