Reports state that Hoolahan has already visited the Liberty Stadium to discuss over a possible move from the League One side.
Whilst neither manager has confirmed the Swans move for the player, new Canaries boss Paul Lambert said “I think that's the nature of the beast. Teams want players – it can happen. What I have to do is get a team here that I think is capable of winning games.
“It's not about any one individual at the club, we have to get the team. If the balance is right in the team, what personnel plays we have to wait and see.”
Hoolahan joined Norwich from Blackpool for around £250,000 last year.