Monaco's league rivals Lyon, who signed Edouard's compatriot and former Hoops team-mate Moussa Dembele for £19.7 million last summer, are understood to be keen on the 21-year-old, who has notched six goals in 11 games so far this season for Neil Lennon's side.
Reports suggest scouts from Les Gones will make several trips to Glasgow this season to run the rule over the former Paris Saint-Germain youngster.
The club is understood to be closely monitoring the player's form for Celtic, having scored 39 goals in 92 appearances for Celtic since his arrival, initially on loan, from the French capital.
Ironically, Edouard could replace Dembele at the Groupama Stadium, with the ex-Fulham and Celtic hitman linked with Juventus and Arsenal in recent months.
Lyon have just two out-and-out centre forwards in Dembele and Amine Gouiri, although Maxwel Cornet, Memphis Depay and Bertrand Traore can all play there if required