Karius' stay in Turkey is set to last two years, but fresh reports had indicated that Besiktas were keen to send the former Mainz star back to Merseyside in exchange for out of favour forward Divock Origi.
The 25-year-old joined the Turkish outfit in the summer on a 2-year loan deal after Liverpool secured the services of Alisson Becker from Roma.
The Liverpool Echo has since rejected those claims, revealing that no option exists in Karius' Besiktas contract which would entitle the Turkish side to offload him at their discretion.
Sources add that the Besiktas board and management have faith in Karius and maintain that the goalkeeper is happy in Istanbul.
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"Complete nonsense", Florian Goll told SID.
Besikta´s goalkeeper Loris Karius throws out the ball during the UEFA Europe League Group I football match Malmo FF v Besiktas in Malmo, Sweden on October 4, 2018.
"It's a fact that Loris is the number 1 at Besiktas and since he made his debut at the club he played in every game and showed good performances".
But according to the Mail's Dominic King on Tuesday morning, even if Besiktas were unhappy with Karius' form and looked to end his time in Istanbul, "it can't happen".
"No thanks, you can keep him free of charge", one fan tweeted.