The 22-year-old enjoyed a productive 2019-20 campaign for his French club, scoring four times and providing seven assists in 36 appearances in all competitions.
Ikone still has three years left to run on his contract with Les Douges, but the France international could allegedly seek pastures new ahead of the 2020-21 season.
According to Le 10 Sport, Chelsea have held talks with Lille over a potential move, and the Ligue 1 club are taking the interest from Frank Lampard's side 'very seriously'.
The report, though, claims that Christophe Galtier's side are yet to receive a significant offer for the Frenchman.
Ikone came through the youth system at Paris Saint-Germain but only made seven first-team appearances for the capital giants before arriving at Lille ahead of the 2018-19 season.