The report claims that the La Liga outfit have already processed the payment and that Fenerbahce have received the fee.
Nani has a £7 million release clause which remains active until the end of the month and he is now expected to undergo a medical with Valencia before completing his deal after his Euro 2016 campaign.
Nani has of course won four Premier League titles in the past and Everton were also in the race to sign the Portuguese international.
The 29-year-old joined Fenerbahce on a three-year deal from United last season and despite having an impressive league campaign he fell out of favour with head coach Vitor Pereira.
Nani is currently on international duty with Portugal and has started all of his national teams games over the course of the European Championships.