The Turkey midfielder was linked with Galatasaray and Fenerbahce over the summer, though ultimately has remained with Inter - even with the Super Lig transfer window still open this week.
His father, Huseyin, told Hurriyet: "God only knows. Right now, Hakan is happy with his club, he's continuing to work at Inter. He already has a contract for another two years.
"There's no question of a transfer."
Calhanoglu Snr was reacting to comments made by Galatasaray coach Okan Buruk over the weekend, when he said: "Hakan was a player we really wanted.
"He's a huge Galatasaray fan. He made a big statement about making a big sacrifice in the future. We made another attempt last week, but Inter said they weren't willing to sell him. They said they would if we offered a much higher price than usual. We made an attempt."