However, Adams was unable to stop the team from being relegated to the Championship following a three-season spell in the top flight.
Former Cardiff City boss Malky Mackay is understood to be the favourite to take charge of Norwich as they look to return to the Premier League.
"It will probably take a little longer but not a lot," McNally is quoted as saying by Sky Sports News.
"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."
Norwich's Premier League campaign ended with a 2-0 defeat at home to Arsenal on May 11.