The report goes onto state that the Netherlands international, who left United to join Fenerbahce last summer, is understood to be unhappy in Turkey.
Chelsea are on the hunt for a new striker following a string of disappointing performances from both Radamel Falcao, and Loic Remy.
Former Manchester United star and football pundit Rio Ferdinand revealed that he believes his former side made a big mistake selling Van Persie over the summer.
“The likes of Robin van Persie guarantee you 15 goals a season,” Ferdinand said speaking on BT Sport 1 after the goalless draw between Manchester United and Chelsea.
The experienced striker created 21 assists and scored 58 goals in a 105 games for Manchester United last season.
Van Persie has one assist and 12 goals in 28 appearances for Fenerbahce this season. Fenerbahce take on Kasimpasa in their next Turkish Super Lig game.