Mourinho gave Karanka his start in coaching as his assistant with Real Madrid.
Karanka told Marca: "I know the capacity that José has and, since he signed, I am one of those who think that some titles are going to be won.
"This year, not only the Premier, all the Leagues are more open than ever. Incredible results have been seen. They themselves were beating West Ham 3-0 and finished 3-3, Aston Villa scored seven against the 'Pool' ... I hope the Premier can be won, but, if it is not the League, some title will be achieved."
On Gareth Bale, Karanka continued: "I think he is a good reinforcement for Tottenham ... and for Birmingham if it had been possible [laughs].
"We are not going to find out now. He has not had a good time in Madrid from what has been seen from the outside, but, in an environment in which he feels comfortable, we're seeing his improvement and in the future it will be seen even more."