HITC Sport understands that a second bid for the Turkey international has been knocked back.
The Turkish star is one of a number of front-men that the Hammers are actively working on, with the view of getting at least one – preferably two - in by next week's transfer deadline.
The 30-year-old joined Gala in 2012 from Trabzonspor and has become their leading striker with 57 league goals in that time, but now West Ham are hoping to prise him away and offer him a Premier League stage on which to perform.
They saw a bid of £3.5million rejected earlier this month and now a new bid of £5million has also been rebuffed by the Turkish giants.
HITC Sport understands that West Ham will return with a third bid, whilst they continue to look at other forward targets including Simone Zaza, Emmanuel Adebayor, Nikica Jelavic and Victor Moses.