The Bluebirds were keen to lure the England Under-21 international to South Wales from Blackpool after having an £8m bid accepted.
However, Ince has now opted to stay in the north-west, so City boss Malky Mackay is switching his attention to the Black Cats youngster instead.
Sunderland are in no hurry to lose Colback though, with the versatile midfielder one of the few players to have been praised on a regular basis by Paolo di Canio since he took over at the Stadium of Light.
However, the 23-year-old, who is valued at around £2.5m, is believed to be unhappy with the club's latest contract offer as he is still earning considerably less than many of his team-mates.
Colback is also interesting former Sunderland manager Steve Bruce at Hull City and they could rival their fellow Premier League newcomers for his signature if he becomes available.