A number of players have been tipped to leave Carrow Road following their relegation from the Premier League, including Robert Snodgrass and goalkeeper John Ruddy.
However, chairman Alan Bowkett has insisted there is no pressure on the club to sell their main men and has assured Adams that nobody will leave against his wishes.
Norwich are looking to bounce straight back up at the first attempt and Bowkett says there are in a good position to challenge for promotion.
"Neil Adams has already been told that if he wants to keep all the players that are here, then we have the financial stability to do just that," he said, quoted in the Daily Star.
Adams finished the season in caretaker charge and Norwich insist he was their first choice to take on the role permanently, despite reportedly considering the likes of Malky Mackay and Gianfranco Zola.
Chief executive David McNally said: "We looked at the market extensively but in the end we realised that Neil was the outstanding candidate.
"He was the first one to be offered the job and no-one else turned the job down.
"Our ambition is to get back to the Premier League and we have appointed Neil with that very much in mind."