The report claims that the Hammers were offered Van Persie at a cut price deal but that they decided not to pursue the former Premier League winner.
The report also states that Van Persie has been offered to recently promoted Middlesbrough who are interested in bringing in experienced players.
Van Persie joined Fenerbahce from Manchester United last season and is reported to be on £240,000-a-week with two-years remaining on his current deal.
The Netherlands international scored 16 times in the league last season helping the Yellow Canaries finish as runners-up and book a place in the Champions League.
Van Persie has years of experience playing Premier League football at Arsenal and Manchester United.
Fenerbahce have not commented on the rumours and have previously stated that they intend on keeping the 32-year-old striker at the club next season.