The report states that Mata is unhappy with the way he has been treated by manager Jose Mourinho and wants out at Old Trafford.
Mata was surprisingly substituted off after just 30 minute on the field during the Community Shield clash against Leicester City last week. The Red Devils went onto win following a debut goal from Zlatan Ibrahimovic.
Fenerbahce are in pursuit of a new attacking midfielder to replace the likes of Diego Ribas and Luis Nani who left over the transfer window.
Mata provided 11 assists and scored 10 goals last term but has a frosty relationship with recently appointed manager Jose Mourinho. The Portuguese tactician previously sold him to United while he was in charge of Chelsea in 2014.