The Super Lig club can offer the Mexico international Champions League football next season after again winning the Turkish league but his £145,000 per week wages are likely to be a large stumbling block.
Hernandez has just 12 months left on his contract with West Ham and has already admitted on a youtube video that he looking for another club but would see out the remainder of his contract if that was not possible.
The Hammers would need to have a replacement in place to be able to sell Hernandez who they hope would raise around £8m. The 31-year-old has made 61 appearances of which 36 were starts with 16 goals from all competitions.
The striker joined the Hammers from Bayer Leverkusen two years ago for just over £16m.