The goalkeeper signed a two-year deal with the Super Lig side after Liverpool brought in Roma's Alisson as his replacement.
A UK newspaper this week quoted Karius as saying he is being asked for photographs by female supporters in Istanbul.
"I did not have this many fans in England and I can say most seem to be female," Karius was quoted as saying.
"Whenever I am out and about in Istanbul whoever recognises me wants a photograph."
But Karius, who has made a single appearance for Besiktas, posted on social media to deny making the comments.
Since arriving in Turkey I haven't had any interviews. The news and quotes that have been published are not true. That's something I wanted you to know.— Loris Karius (@LorisKarius) September 13, 2018
Yours, Loris Karius
"Since arriving in Turkey I haven't had any interviews," Karius wrote on Twitter.
"The news and quotes that have been published are not true. That's something I wanted you to know."
The German goalkeeper last played a competitive game for Liverpool in the Champions League final defeat to Real Madrid, where he was at fault for two goals. He was given a chance to redeem himself during the summer by Jurgen Klopp, but committed errors in friendlies with Tranmere Rovers and Borussia Dortmund.
The addition of Alisson saw Karius fall down the pecking order, with Simon Mignolet serving as backup at Anfield as Karius was allowed to leave to join Besiktas on loan.