Mackay, who played over 200 times for Norwich during a six-year spell at Carrow Road, was one of several names linked with the manager's position following Paul Lambert's move to Aston Villa last week.
The Cardiff manager has now insisted that he is happy with the Welsh club, however, despite being "flattered" by the Canaries' apparent interest. In a statement released by his agent, he said: "I have started a long-term project and want to stay and finish it."
He added: "I am very flattered to be linked with the vacancy at Norwich City. They are and always will be a club close to my heart.
"I have a lot of good friends within the club and great respect for Delia Smith and her husband Michael Wynn-Jones. David McNally, the club's chief executive, has handled this situation well and is guiding Norwich in the right direction.
"However, I have started a project at Cardiff City. We have put in a structure for long-term success at this football club and we are still working on that. I am fully committed to our football club and the challenges ahead."
While Mackay's statement will reassure Cardiff fans, the timing of it is a little strange given that Canaries chief executive McNally appeared to rule the 40-year-old out of contention. McNally claims the Canaries, who finished 12th in the Barclays Premier League last term, are only looking for a manager with top-flight experience, whether it be in England or abroad.
"The search is certainly a European search,'' McNally told the Eastern Daily Press. "We are looking for somebody who has got top-league experience.
"I don't think the candidate necessarily has to have Premier League experience - but they have to have top-league experience. If, for example, you have managed in Serie A, La Liga, the Bundesliga, they are some of the toughest leagues in the world too.
"So why on earth if there is a candidate in one of those leagues who was available and we felt was right for us should we say no to them just because they haven't managed in the Premier League?"