McNally also confirmed a position of technical director will be part of the new management structure at Carrow Road.
The Canaries placed youth team coach Neil Adams in charge for the final five games of the Premier League season following the sacking of Chris Hughton on April 6.
But Adams was unable to prevent the Norfolk club from losing their top-flight status, with the board admitting to making mistakes and feeling "frustrated, hugely disappointed and embarrassed" by relegation.
McNally revealed Adams is "a credible candidate" for the managerial vacancy, however the hot favourite for the job is former City captain Malky Mackay who is odds on for the position with bookmakers.
Last Friday, it was announced that Mackay had dropped his legal claim against his sacking with Cardiff City after reaching a settlement with the club.
The Scot issued a conciliatory statement through lawyers in which he apologised "without reservation" to Tan.
Celtic boss Neil Lennon and Gianfranco Zola also being linked to the position.
The club had hoped to make an announcement "within a week" but after Sunday's deadline passed, McNally and joint majority shareholders Delia Smith and her husband Michael Wynn Jones appeared on Radio Norfolk for a special phone-in on Monday morning.
When asked if Norwich have made an approach for a new manager, McNally said: "No we haven't. We are still in the process.
"We announced the search started after the season ended. It is probably going to take a little longer.
"We are talking to a short list of candidates. We are taking a few days longer than we indicated but it is only days.
"Neil is definitely a candidate and a credible candidate. He accepted the poisoned chalice and managed the team through a very difficult period."
On the possibility of appointing fans' favourite Mackay, McNally added: "As a man I don't know him very well, Delia and Michael probably know him better from his time at the club. I know his place in Norwich City folklore and his success as a Championship player.
"I think it's unfair on any candidate to confirm or otherwise because somebody is going to get the job and others won't and I don't think that's right."
Many fans have accused the board of not acting sooner by replacing Hughton in January but celebrity chef Smith responded: "There wasn't anybody else out there.
"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?"
She added: "We got it wrong. It might have happened that if we got a caretaker manager in that we might have stayed up. But there was no guarantee."
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- Chris Hughton