Karius made two mistakes that helped Real Madrid beat Liverpool 3-1 in May's Champions League final in Kiev and found himself loaned out to Besiktas.
Reports have emerged in recent days suggesting the Turkish club were looking to end the loan in January but his agent Florian Goll claimed that was not the case.
"Complete nonsense," Goll said in quotes reported by FourFourTwo.
"I wonder where such things come from. This news is absolutely untrue.
"Loris is on loan to Besiktas for two years - that's the situation. The club has no intention of ending this loan contract prematurely.
"It's fact that Loris is the clear number one at Besiktas, he played every game and showed good performances."
Karius appeared to have his own say on the rumours in a since-deleted Instagram post from Tuesday evening. On a picture of himself drinking coffee, he added the caption: "Coffee first, media's bulls*** second".
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