The Dane has been linked with the Old Trafford side but says all his energy is focused on ensuring the LOSC reach Europe's premier club competition
The Denmark international, 25, arrived in France less than a year ago from Wolfsburg but has been so influential that the Old Trafford club have taken an interest in his services, according to local paper La Voix du Nord.
Kjaer, however, has indicated that he is presently only aiming to do his best for his current employers.
“It’s always nice to know about interest from other big clubs but to be honest rumours like that are not in my thoughts at all right now,” he told BT.
“All my focus and energy is on the Lille games and for me personally my concentration is all about achieving my big goal to play in the Champions League with Lille next season.”
The former Roma man was once more influential as Lille kept a 21st clean sheet of the season in only 34 league outings on Sunday, as Rene Girard’s men drew 0-0 away to Olympique de Marseille and firmed up their grip on third place.
Speaking to Goal, Kjaer indicated: “That one point means that we have qualified for Europe, which was the goal of the club at the start of the season. But now we want more than that. Now we definitely want third spot and the chance of playing in the Champions League.”
After a man-of-the-match display at Stade Velodrome, the Dane said that more important than his individual display was that of the side.
“It’s a result of LOSC playing as a team and being really good in terms of our defensive organisation,” he continued. “It proves that as a team, as well as I in my personal performances, have held a high level of consistency this season, and that makes me proud.”
Lille currently lie third in Ligue 1, eight points behind second-placed Monaco but crucially seven better off than closest challengers Saint-Etienne with only four matches remaining.