The 24-year-old is enjoying an impressive loan spell from West Brom and grabbed his first goal for the Canaries to earn a 1-1 draw with Leeds at Carrow Road on Saturday.
His stay expires on January 4 but boss Paul Lambert wants the player to stay - and Barnett would welcome the prospect too.
He told the Evening News: "I think I'd be stupid not to. There are a lot of players who would love to come to Norwich and I'm one of them, so it's a possibility but we have to wait until January.
"It's a great feeling and this is a massive team and we're going in the right direction.
"I think it's nice to be loved and if someone wants to take interest in you. But at the moment I've not heard anything and I have to wait until January and see what happens. I don't know what's going on."
Source: PA
Source: PA