The 32-year-old joined Leicester from Portuguese club Sporting Lisbon for a fee in the region of £27m in 2016, but has spent time away from the club on multiple loans since the start of 2018.
Slimani has now entered the final year of his contract with the Premier League club and has been linked with a move away from the King Power Stadium.
According to French radio station RMC, Ligue 1 club Lyon are interested in acquiring the services of the Algeria international and have begun talks with the player.
Slimani, who spent last season on loan at Monaco, is keen on the prospect of joining the French club.
Leicester could even allow the player to leave the club on a free transfer despite having a year left on his contract, to facilitate the move.
However, Lyon would likely only move for the striker when one of their attacking players have left the club.
Slimani may be hoping for the opportunity to rekindle his career at Lyon.
