The report states that Everton’s interest in the former Manchester United star has intensified and that Nani is making preparations to leave Istanbul over the summer.
The 29-year-old is understood to have an €8 million release clause included in his contract.
The Portuguese international won four league titles and the Champions League at United but left the club after falling out with current head coach Louis van Gaal.
Nani joined Fenerbahce for £4.25m on a three-year deal over the summer transfer window and despite being well settled in Istanbul his recent interview suggests that he would consider a return to England.
Everton are considering making a £6 million move for the experienced winger according to Talksport.
Nani has 13 goals and 12 assists in 46 appearances for Fenerbahce this season.