McNally, who has worked for the club's owners Delia Smith and Michael Wynn-Jones since 2009, was bombarded with messages from angry fans on Twitter following the side's 1-0 defeat to Manchester United on Saturday.
Combined with other results, the loss left the Canaries four points from safety in the Premier League table and means that they will definitely be relegated if Sunderland defeat Everton on Wednesday.
Replying to one fan at 8.35pm on Saturday, McNally reportedly wrote: "That's okay and I understand your view. I've resigned tonight and I hope that the club can now progress."
Hours later at 1am, he appeared to backtrack on the decision however, writing: "I take back what was said earlier. I remain fully committed to NCFC and to Delia and Michael & I've not resigned. My apologies."
The Canaries have thus far failed to comment on McNally's position with the club.