The daily sports paper states that negotiations are at an advanced stage and that Nani is expected to leave over the Summer.
Manchester United have also been closely linked with a move for the 29=year-old. United are reported to have already agreed personal terms with their former player according to Turkish media outlet DHA.
United would have to offer more than they sold Nani for just last year if they are to bring him back to Old Trafford.
Nani has a £6.2 million release clause for sides from the Premier League, La Liga and Serie A which would be more than the £4.2 million United received for him.
The experienced winger does still have another two-years remaining on his Fenerbahce contract but is reported to have fallen out with manager Vitor Pereira.