The Hammers are after the Canadian international, who was a regular in Turkey under Bilic.
Recently West Ham United were seemingly set to sign Joey Barton on a free transfer. That deal never came off and now they are looking into potential other avenues.
Hutchinson is an energetic midfielder who can also play at full-back and would be a shrewd signing for the club at the right price.
According to a report in Fanatik the club are willing to pay a fee in the region of €5 million (£3.5 million) for the player, who was a regular feature under the management of Slaven Bilic in the Turkish capital.
Would he be a good signing?
Hutchinson maybe 32-years-old but he remains in terrific shape for a man of his vintage and would provide excellent cover in numerous positions.
Reece Oxford impressed for West Ham against Arsenal next week, but considering his age they will need another option for the midfield, where they are currently perhaps a man short.
The fact Hutchinson can also play at right-back, and at times left-back, is an added caveat of the player.
Bilic trusts him and Hutchinson might be a good addition to the West Ham crew, however, they might want to pay a smaller fee than what is being quoted currently.