The Yellow Canaries have been closely linked with Mirallas recently and the Hurriyet newspaper claimed that Fenerbahçe wanted to complete the transfer for €13 million.
Mirallas joined Everton from Olympiakos for £6.7 million in 2012 and has a contract with the Toffees until 2016.
The 27-year-old midfielder has scored nine times in 46 games for the Belgium national side and featured in the 2014 World Cup in Brazil.
The Belgium international only has a year remaining on his contract is reported to be stalling on renewing his deal with Everton.
The Telegraph report that West Ham are closely interested in the experienced midfielder.
The Istanbul giants are unlikely to make another signing until after the Champions League preliminary play-off stages against Shakhtar Donetsk at the end of the month.