The Dane has impressed in Turkey.
Chelsea have a new manager arriving this summer, with Italian national team coach Antonio Conte arriving at Stamford Bridge to take over from interim boss Guus Hiddink.
The defence will need to be strengthened. John Terry might be on his way out whilst Kurt Zouma is suffering with a long-term injury.
Now a name has been suggested as interesting Chelsea for the summer.
The report claims that Fenerbahce would be interested in selling the player if Chelsea were to make a bid in the region of €15 million (£12.1 million) for the player, who Conte will know from his time playing in Italy with Palermo.
Kjaer however has recently made it clear he wants to stay, through his agent. Lars Hendel told Turkish-Football last month:
"Simon is only focused on Fenerbahce and helping the club to win the title that they deserve.
“Simon is happy at Fenerbahce and is not looking for a new club.”
Kjaer has played 36 times for the Turkish club this season, after joining the club from Lille in the summer.