Bilic's revolution has got off to a flying start and his side, glittering with stars like Dimitri Payet, are well poised for an assault on the European places.
But with injuries constantly unsettling his side, the former Croatia boss has been linked with a host of players before the January transfer window closes on Monday.
Arslan was one of the big success stories of Bilic's tenure at the Turkish giants after the midfielder went on to star following his bargain transfer from Hamburg for less than £500,000.
Arslan scored a memorable goal for Bilic's side as they knocked Liverpool out of the Europa League last season.
And according to Turkish sports website Fanatik Bilic was rumoured to have promised Arslan the prospect of Premier League football should he take charge of an English side.
West Ham have also been linked with Arslan's teammate Tore since Bilic's arrival.
The former Chelsea youth prospect was close to a move to East London in the summer and Bilic told the same website: “The West Ham fans would have loved him but it did not happen we could not agree a deal.”
With the transfer window in full swing, Bilic has spoken out on fresh links to the duo but is keeping his cards close to his chest.
"I have heard the rumours linking us with Gökhan Töre and Tolgay Arslan but I do not want to comment on that right now," Bilic told Fanatik.
So there you have it, West Ham could well be in the running to do some business as they push for a shock tilt at the Champions League places.
It would be a welcome boost for supporters who have been left wondering just how good their season could have been had they not suffered a glut of injuries to key players like Dimitri Payet, Manuel Lanzini, Diafra Sakho, Andy Carroll and Winston Reid.