Lambert is on the brink of becoming the new Aston Villa manager after resigning from his position at Carrow Road.
McNally confirmed that the club have begun the process of searching for a new manager but refuted claims that Neil Lennon or Cardiff City boss Malky Mackay have been approached.
"It is interesting I have seen it reported we have contacted [Cardiff and Celtic], but we haven't and I would like to put that on record," McNally told Sky Sports News.
"Celtic and us get on very well but I can confirm that no approach has been made to Neil Lennon. We would go straight to them quietly and privately."
Lambert had been in charge of the Canaries since 2009.