The newspaper reports that the Blues have been keeping close tabs on the Denmark international all season.
Kjaer joined Fenerbahce on a €7.65 million transfer from Lille which is a record fee for a defender in Turkey.
The 26-year-old defender was one of the most impressive players for the Turkish Super League runners-up last season.
Kjaer still has another three-years on his deal with Fenerbahce and a source close to the player told Turkish-football.com that despite the transfer rumours Chelsea have not made an offer.
The Blues could face competition from Manchester United who sent sent scouts to watch Kjaer during his international friendly for Denmark against Iceland recently.
PSG and Atletico Madrid were also reported to have send scouts to keep tabs on the Denmark international.
Fenerbahce finished the league as runners up and will compete in the Champions League next season.