The report states that Jose Mourinho is keen on bringing in the Denmark international to strengthen his defensive line next season.
Fanatik claimed earlier in the season that United sent scouts out to watch Kjaer during his international friendly for Denmark against Iceland.
French giants PSG and La Liga outfit Atletico Madrid were also reported to have send scouts to keep tabs on the Denmark international.
Chelsea have also been closely linked with Kjaer over the past few months and have been keeping tabs on the Denmark international according to Fanatik.
However, a source close to the player told Turkish-football.com that despite the transfer rumours Chelsea have not made an offer.
Kjaer still has another three-years on his deal with Fenerbahce and the Istanbul giants are keen to keep hold of their star man who joined from Lille last season.