If he joins Inter, Ince would follow in the footsteps of his father Paul, who played for the club between 1995 and 1997.
"I'm not an Inter player yet," Ince told Sky Italia. "I'm very happy to be here two or three days in the meantime.
"Inter is a fantastic squad and Italy is a great country, where I have many fond memories.
"I remember the San Siro with affection, players like [Javier] Zanetti, [Massimo] Paganin and [Aron] Winter. We lived in Como. It's marvellous to be here at 22."
Ince spent the second half of last season on loan at Crystal Palace.