The Northern Irishman was on Friday morning tipped as a replacement for Paul Lambert, his former Celtic team-mate who has offered his resignation ahead of his expected move to Aston Villa.
Cardiff manager Malky Mackay, another former Celt, has also been linked with the position at Carrow Road, but McNally told SkySports: "It is interesting because I have seen reported that we have contacted both of their clubs about their managers. We haven't and I would like to put that on record."
He added: "Celtic Football Club and Norwich City get on marvellously well, we had a great day here last week celebrating Adam Drury's testimonial, the two sets of supporters get on brilliantly.
"I can confirm that no approach has been made for Neil Lennon.
"If we were interested in talking to them about Neil, he's a great manager, we would go straight to them quietly and privately, we wouldn't announce it through the media and Dermot Desmond (Celtic's majority shareholder) would be the first to know."
Press Association Sport understands the Parkhead club would not entertain any approach for Lennon, who won his first Clydesdale Bank Premier League title as manager last season.
Source: PA
Source: PA