Per the source, the Italian giants are making preparations for the possibility of defenders Albiol and Koulibaly parting ways with the club over the summer.
Kjaer is no stranger to the Serie A having played for Serie A rivals Roma in the past.
The Blues were reported to be close to agreeing a deal with Kjaer back in May but the player ruled out a move this summer.
The Yellow Canaries value the Denmark international at €15 million and would not even consider offers below his asking price.
The 27-year-old centre back joined the Yellow Canaries on a €7.65 million move from Ligue 1 outfit Lille last summer.
Kjaer has established himself as a first-team regular in the Fenerbahce side last season and has one goals and two assists in 57 international appearances for the Danish national team.