The report claims that the Yellow Canaries have been keeping tabs on the Belgium international all season.
It is not the first time Fenerbahce have been linked with Mirallas either. The Istanbul giants were also reported to have made an enquiry for the 26-year-old midfielder last season.
Mirallas faces an uncertain future at Everton after being relegated to a substitute under the stewardship of Roberto Martinez last season.
Martinez has since lost his job but it remains to be seen what his successor has in store for the attacking midfielder.
Mirallas missed out on being picked for the Belgium Euro 2016 side as a result despite making the World Cup side two years ago.
The Everton midfielder still has another two-years on his contract and is valued at around £10 million.
Fenerbahce would be able to offer Mirallas first-team and Champions League football if he were to make the move.