The 20-year-old's current contract is not up for renewal until 2005, but the club have been impressed with his efforts.
AZ have proposed a new deal that would tie him to the club for another three years, and Zwarthoed has gone away to consider the offer.
The Dutch Under-21 international is the current understudy to Henk Timmer, but AZ clearly feel he will make the grade in the coming seasons.