BBC journalist David Ornstein reported that the Gunners are considering Kjaer and Turkish international defender Omer Toprak as an alternative for transfer priority Mustafi.
Turkish sports newspaper Fanatik meanwhile claim that Arsenal are considering a £12 million move for the Danish international.
A source close to the club told Turkish-football.com that while Arsenal have made an enquiry, Fenerbahce have made it clear they do not want to sell and would not consider offers below £15 million.
The Yellow Canaries want to keep hold of Kjaer who has settled in well since his move from Lille and the defender does have another three-years left on his contract.
The Istanbul giants have already turned down approaches from Napoli and Chelsea for his services and unless an offer is made that exceeds their valuation it is unlikely he will leave this summer.