The Canaries are currently 11th in the Premier League but the Norfolk side are only four points behind seventh-placed Everton.
The club's chief executive David McNally has admitted that there will not be large amounts of money available to Lambert but is determined to provide the Scot with funding.
McNally said: "We are a co-operative and any spare cash goes to the football manager. While we are here managing the club, that will be the case."
Lambert has enjoyed two promotions during his time at Norwich City.