The 28-year-old, who joined the Championship outfit from Al Ahly last month, has scored three goals in his five matches for Hull.
"I want to delight the Hull fans who have supported me since I came to England. I am having a great life here and I want to continue my career in Hull and hope not to go back to Egypt now," he told The Mirror.
"I have a big need to score more goals for this coach, who has shown so much faith in me, and this team."
It is understood that Gedo would cost in the region of £3m.