Officials at Carrow Road expect to announce new managerial appointment in the coming days, following their relegation from the Premier League.
The Canaries finished the season in 18th place, having only secured eight wins and 33 points in 38 games.
Manager Chris Hughton was sacked in April, after a 1-0 defeat to West Bromwich Albion left his side only five points clear of the relegation zone, and under-18 coach Neil Adams took control of the first-team on a temporary basis. Adams struggled to have an impact - failing to win any of his five games in charge - and, after an impressive, but futile, draw to Chelsea, Norwich were all but relegated to the Championship.
And, on the day that the Canaries lost 2-0 at home to Arsenal to close the season, a statement was released on the official website to announce that the club are close to making a new managerial appointment - with Adams one of many possible candidates.
'Everyone at Norwich City shares our fans' deep disappointment that we have been unable to secure Premier League status for a fourth consecutive season, despite the best efforts of players and staff at Carrow Road and Colney.
'We'd like to thank our fantastic supporters for their unswerving and passionate backing home and away in what has been a very challenging season for everyone connected with Norwich City. As always, the 'Yellow Army' has been a credit to their Football Club and to the county of Norfolk.
'The Board fully accepts that mistakes have been made which have contributed to our relegation.
'It is always our stated strategy to improve the squad in every transfer window. We backed the manager with the funds to sign a number of players this season with every intention of improving the squad, but unfortunately that improvement did not materialise.
'Work is already under way to learn from the experiences of this season and to prepare for a busy summer as we focus all of our energies and resources on competing in the Sky Bet Championship next season.
'The next step is to confirm who will be our manager next season and this process is under way now. Neil Adams, who has done an admirable job in difficult circumstances, is one of a number of candidates the Board is talking to.
'The Board will confirm who our manager will be in the 2014-15 season in a statement to supporters within a week.'
Former Cardiff City boss Malky Mackay, who settled his dispute with owner Vincent Tan this week, is a strong favourite for the role, whilst another ex-Watford boss - Gianfranco Zola - is also believed to be wanted by the club. Although Adams did not do himself any favours with his record in the top flight, chief executive David McNally suggested that the former youth coach is a strong contender.
In an interview with BBC Radio Norfolk, McNally said: "Neil is a credible, serious contender.
"He's done a very good job in very difficult circumstances. Talk about giving him a poisoned chalice.
"What we've seen is there is a manager of the future there. But we are talking to other people. There are three or four names."
Adams himself has expressed his delight at being considered for the role, and the 48-year old has just a week to wait to find out whether he will be in a job come July 1.