He said: "I love it here. I've got a great rapport with people here and I'm not going anywhere."
Norwich chairman Alan Bowkett also believes there is no chance of Lambert jumping ship to take over at Burnley - as the two sides will be in the same division next season.
Bowkett is confident the sides will be meeting in next season's Championship.
He told the Norwich Evening News: "Paul is staying with us and we have every confidence that if Paul were approached and offered the position he would wish to stay with us.
"Paul is so enthused about working here. I think he wants to work with the fans. He is incredibly motivated by their support and encouragement. I think he would find it extremely difficult to leave.
"Equally he is an ambitious individual who wants to achieve things. To do that, he's got to start winning and I'd like to think he's going to win here and get us promotion and get us into a promotion position next year.
"To be perfectly brutal, it is probable that we will be in the Championship next year and it is probable that Burnley will be in the Championship next year and I think Paul would prefer to work for the Norwich fans than the Burnley fans."