The report states that Fenerbahce’s sporting director Giuliano Terraneo will fly to England to hold talks with Everton if Fenerbahce eliminate Shakhtar Donetsk in the UEFA Champions League qualification round.
Fanatik also claim that the Istanbul giants have already had a €10 million offer rejected by Everton and that they will submit an improved offer.
The Yellow Canaries are preparing a shortlist of targets following reports linking Moussa Sow with a move away from Istanbul.
Mirallas joined Everton from Olympiakos for £6.7 million in 2012 and has a contract with the Toffees until 2016.
The 27-year-old has 25 goals and 23 assists in 90 appearances for Everton in all competitions.
Mirallas has scored nine times in 46 games for the Belgium national side and featured in the 2014 World Cup in Brazil. The Belgium international provided three assists and scored 11 goals for Everton last season.