Bilic was widely praised in Turkey for his handling of the Arslan transfer last season while in charge of the Black Eagles.
The Croatian manager signed Arslan for just €500,000 from HSV and the 24-year-old soon established himself as a key member of the team scoring a memorable goal in the Europa League Round of 32 victory over Liverpool.
Bilic was rumoured to have promised Arslan the prospect of Premier League football should he take charge of an English side during the negotiation process.
Bilic told Fanatik: “I have heard the rumours linking us with Gökhan Töre and Tolgay Arslan but I do not want to comment on that right now.”
Arslan was ruled out of the first half of the season due to injury but has since recovered and is expected to return to full fitness soon.
Besiktas are currently second in the Turkish Super League but have two games in hand and will go top if they win both matches.