The former Wolfsburg player had his career somewhat derailed after an unsuccessful stint at Roma but after making the move to Lille from Germany in the Summer for 2.5 million euros, he has helped the team to third position.
Manchester United are believed to be after a replacement for Namanja Vidic who is leaving for Inter Milan at the end of the season and could look at recruiting the 25 year-old.
In an interview with Danish paper BT, Kjaer responded to these rumours."It is of course flattering to be linked with big clubs but I am not wasting my thoughts on rumours with other clubs."
"I am spending all of my efforts and keep my focus entirely on reaching my goal that we will qualify for the Champions League next season."
Kjaer has made 30 appearances for Lille this season and with 5 games left, they sit in the last qualification spot for the Champions League, 6 points behind AS Monaco and 7 points ahead of AS Saint-Etienne.