The 22-year-old joined Lille in 2017 and has gone on to make 106 appearances for the French club, with his contract due to expire in the summer of 2022.
Soumare has been valued at £30m and reports suggest that the Frenchman has been on the radar of the Foxes for more than a year, during an impressive rise from Paris Saint-Germain B to the top of Ligue 1.
According to the Daily Star, Brendan Rodgers's club have passed Man United and Spurs in the race for the youngster's signature, in the hope he can follow in the footsteps of fellow France international N'Golo Kante.
The midfielder has helped Lille to boast the best defensive record in Ligue 1 this season, conceding just 19 goals in 32 games.
Soumare has played 37 games in all competitions for Christophe Galtier's side this season, with Lille sitting three points clear of second-placed PSG with six games to play. body check tags ::