Lambert has become one of the most sought-after young managers around after masterminding the Canaries' rise from League One obscurity to mid-table in the Premier League inside two years.
Some Norwich fans fear the managerial merry-go-round that could result from the England vacancy being filled this summer will lead to Lambert being lured away from Carrow Road.
But, speaking to tourism business leaders during an event at the club's stadium, chief executive David McNally said: "Paul is happy here.
"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."