The former Canaries defender was quickly installed as a strong favourite for the Carrow Road post once Paul Lambert took the decision to take the reins at Aston Villa.
Mackay spent six years with Norwich during his playing days and admits the club still holds a special place in his heart.
He is, however, keen to distance himself from the rumours suggesting he could be about to return to Norfolk.
Having only been appointed Cardiff manager in the summer of 2011, and having led them to the Championship play-offs during his first season, Mackay is determined to 'finish the exciting project' he has undertaken in South Wales.
In an exclusive statement passed to Sky Sports News HD, he said: "I'm very flattered to be linked with Norwich as it's a club close to my heart from my playing days there.
"I have very good friends within the club and greatly respect Delia Smith and her fellow majority shareholder Michael Wynn Jones.
"Norwich are moving in the right direction but I want to finish the exciting project I've started at Cardiff where we've a structure in place geared to long-term success.
"I've a great relationship with our chief executive Alan Whiteley and the club's owner Vincent Tan is committed to major investment in Cardiff more of which will become apparent later this week.
"I too am fully committed to our football club and I'm ready for the challenges ahead."
Mackay may not have been a prominent target for Norwich after chief executive David McNally revealed the club are looking for a manager with "top league" experience.
McNally insists the position is an attractive one and has revealed that the club will scour Europe in the hope of finding a new manager who can continue Lambert's good work at Carrow Road.
"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?"
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