Lambert has been linked with a number of rival Premier League clubs in recent months after having impressed at Carrow Road.
“Paul is happy here,” McNally said. “It’s his football club, he’s been accepted by the great people of Norwich and Norfolk.
“He’s hugely ambitious. We haven’t let him down yet – we have matched that ambition having gone from 69th position to 12th. We will do all we can to work together for the long term.”
