The Mexican international has struggled to find his best form for The Hammers since arriving from German outfit Bayer Leverkusen last summer.
After a fruitful spell in Germany, where Chicharito seemingly rediscovered the form which made him a regular starter at Old Trafford, he has fallen flat once more at West Ham.
It is once again because the 30-year-old is not viewed as technically good enough to lead a modern Premier League line.
Instead, the striker’s quick movement and fox-in-the-box presence are viewed as invaluable substitute qualities.
Hernandez is not happy with that role, however, and is seeking regular first-team football in Europe.
Hernandez scored his first Premier League goal of the season against Burnley last weekend after suffering five weeks out with a virus.
Besiktas have expressed their interest in securing the striker’s signature.
The Super Lig seems to be a hotbed for out-of-favour Premier League forwards, with the big clubs willing to offer healthy wage packages, first-team football, and a good shot at Champions League football.
It is understood that Besiktas are keen on a loan when the transfer window opens in the New Year.
In such a scenario, they will have an option to buy him at the end of the season.
But The Hammers may only let him leave if Manuel Pellegrini agrees to the deal.
Pellegrini has plenty of options available and Hernandez is some way behind his main front man Marko Arnautovic in his pecking order.
West Ham find themselves 13th in the table after a disappointing 1-1 draw against Huddersfield.
It took Pellegrini’s men five games until they got their first point.
Arnautovic has emerged once more as the talisman, however, notching five goals.
The Hammers welcome Manchester City to the London Stadium in their next league match.