Slimani, 32, spent last season on loan at Monaco and impressed with nine goals in 18 league appearances.
However, Monaco chose not to use their option to buy, leaving Slimani to find another club.
The Algerian international has no future at Leicester and they could even release him from his contract one year early.
Leicester paid a club-record €30m to sign Slimani from Sporting CP in 2016, but he has been out on loan since January 2018.
Lyon could move forward to sign Slimani if they lose one of their offensive players.