The Sun says the Foxes are in talks with the Ligue 2 side, but they will face competition from a host of interested teams.
Diabate is a team-mate of Gregoire Puel, who is the eldest son of the Leicester boss.
Diabate's agent Yacine Ayad has confirmed Leicester's interest, but he refused to release further details.
Ayad told L'Equipe: "Leicester have started discussions between the clubs for Fousseni.
"But at this stage, there is nothing yet done so much.
"Gazelec have received other offers from Ligue 1 and abroad in the past few days."