Norgaard, who signed for Brentford when they were still in the Championship, has been an integral part of the team that has established itself firmly in the Premier League.
With Arsenal having genuine ambitions to win not only silverware but the title, Brentford cannot offer Norgaard the same level of competition and challenge.
The departure of Norgaard, along with other midfielders Jorginho and Thomas Partey, means Arsenal manager Mikel Arteta will be looking to strengthen his midfield with players like Norgaard.
Despite the loss of a key player, Andrews sees a positive side to Norgaard's departure, saying it will allow other squad members to step up and take on new roles.
"Christian has been a huge player for our football club," Andrews said. "He's a leader, a top human being, and I believe he will be missed.
"However, I think this will provide opportunities for others, and I know there are players in our building who will take the opportunity to shine."
Arsenal are also looking to complete a deal for Martin Zubimendi, which will help strengthen their midfield, and have already signed goalkeeper Kepa Arrizabalaga from Chelsea.