Reports in some quarters had suggested that Cole's season-long switch, completed on Wednesday, included a clause with the Anfield club that gave them first refusal on Hazard.
The 20-year-old Belgian international has attracted strong interest from Arsenal in recent times, and previously been linked with the likes of Real Madrid.
Liverpool are familiar with Hazard's ability, having seen him score against them during a Europa League clash in 2010, but Lille's general manager Frederic Paquet has rubbished any suggestion that negotiations for Cole's move involved a discussion of Hazard.
"There is absolutely nothing in that," Pacquet told The Independent. "There is no link between Joe Cole and Eden. There has been no discussion. We know Eden Hazard is interesting some of the best clubs in Europe, but he is here and part of the project."
Hazard's current contract at Stade Lille-Metropole runs until 2015.