Turkish source Fanatik were among many to report the news that West Ham, as well as Aston Villa and Atletico Madrid, were keen on the talented playmaker.
Arsenal are now being credited with an interest as well, as reported by the Daily Star.
Now the player has admitted he is open to leaving Besiktas in the near future. The Turkish midfielder told Fanatik this week:
"My first goal is to win the championship with Besiktas. The second is to play in one of the world's most important clubs.
"I've received offers from Europe, but the conditions were not favourable.
"Until the offers meet my expectations, I do not think I'm going anywhere."
Arsenal would of course be re-signing the player, who they let go as a youngster.
West Ham boss Slaven Bilic worked with the 23-year-old at his former club Besiktas, so also has a personal connection to the deal.
The Croatian boss helped the Turkish international come on as a player last season and West Ham would certainly enjoy bringing in the talented midfielder to the Premier League.
A January move seems unlikely but in the summer it will be no surprise if West Ham make a move to bring him in.