After his loan with Aston Villa last season, Zaniolo is being linked with Atalanta.
But Kırmızı told Radyospor: "As far as I know, Zaniolo does not have the attitude of the type at all: 'I will not play for Galatasaray'. Many things written and told have been exaggerated, Zaniolo is currently one of our players under contract.
"Future? At the moment we cannot say for sure if Zaniolo will go away or if he will stay."
Kırmızı also spoke of former Inter Milan striker Mauro Icardi's future.
He said, "It is absolutely normal that there is interest in Icardi, who is one of the most important players in the world, one of the best attackers of his generation. There is interest from many clubs, not just Arabs, but there is no official offer that I know of at the moment."