Roma, Atletico Madrid, Monaco and Galatasaray also said to fancy ex-Blues man.
Arsenal and Liverpool are among a host of European clubs that are keen on signing former Chelsea forward Salomon Kalou this summer, according to Sky Sports.
Kalou has scored 14 goals and provided six assists in 37 Ligue 1 appearances for Lille this season.
Lille will qualify for the Champions League if they win at Lorient on Saturday, but the 2011 French champions may struggle to keep hold of Kalou regardless.
Arsenal are believed to be long-term admirers of Kalou and Sky Sports claim that the Gunners, along with Roma, Atletico Madrid, Monaco and Galatasaray, are keeping tabs on the 28-year-old.
Kalou has just over two years left to run on his current contract at Stade Pierre-Mauroy.
If they chose to sell, Lille will want to make a significant profit on the £8m that they paid Chelsea for Kalou in July 2012.
Kalou scored 60 goals in 254 first-team appearances during six seasons at Stamford Bridge.
He won one Premier League, four FA Cups, one League Cup and one Champions League with the Blues.
Kalou, who was named in the Ivory Coast’s 28-man provisional World Cup squad earlier this week, has been capped 64 times at senior international level, scoring 23 goals.