Mackay and Gianfranco Zola have been interviewed for the job, while Celtic chief Neil Lennon and Neil Adams - who finished last season as interim boss following the sacking of Chris Hughton - were also among the candidates.
Chief executive David McNally has revealed the club are hopeful that they will soon confirm the identity of their new manager.
"It will probably take a little longer but not a lot," said McNally.
"We are pleased with the way the search is being managed, it will perhaps take a few days longer than indicated but that is days and I'm sure Norwich City fans are more concerned that we do the right thing rather than hit a deadline.
"We've said from the moment we were relegated that we feel frustrated, hugely disappointed and embarrassed that we'd been relegated to the Championship."
Club owner Delia Smith admits that they got 'it wrong' when they sacked Hughton and replaced him with Adams.
"Yeah, we got it wrong. It might have happened that if we got a caretaker manager in that we might have stayed up," she told BBC Radio Norfolk.
"But I would challenge anybody to sit round that table and do what we do and get it right.
"We didn't feel at that time there was anybody out there so we had a decision to make, do we bring in a kind of caretaker, so there were one or two names we were looking at, or go with a manager who is winning home games?"
McNally also revealed the club's intention to appoint a technical director.