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.
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.
But this week the Turkish side have made it clear - the midfielder is going nowhere. Tutto Mercato Web are reporting Besiktas president Fikret Orman as stating:
"I will not change the player in the current season, would be in what we asked the coach. Do not send anyone away, it would only create confusion among the players.
"And if we could win the championship, their value would increase. We will sit to talk to interested clubs at the end of the championship."
Born in Holland the midfielder joined Arsenal in 2008 from AZ Alkmaar and never made an appearance for the first-team before heading to Besiktas in 2012 - where he eventually worked with West Ham boss Bilic.
He has 14 caps for his national team scoring one goal, against his birthplace Holland, in a game that helped knock them out of Euro 2016 qualifying.
It seems then that Ozyakup might become available in the summer but that for now, West Ham, Arsenal and anyone else keen will have to watch from afar.