The Dutchman has nine goals in 16 games for the Eredivisie side.
His time at Forest was not exactly productive. He scored no goals in 14 appearances for the club, despite scoring for fun at previous club Excelsior Rotterdam.
But just hours after signing for his new club Veldwijk scored on his Zwolle debut in a pre-season friendly and that form has continued. He has scored nine goals in 16 appearances for the club since departing Forest.
Now the Dutch club have been discussing the potential permanent signing of the striker.
"The intention is definitely to stay together.
"He has indicated that he is in favor of a longer stay with us. We look now at what construction we can do with one another (over a deal).
"We want to capture Veldwijk on our own (without third-party investment)."
It will be interesting to see where Forest go with this deal.
Veldwijlk is still contracted with Forest until 2017 and with the majority of their current strikers only loan players the club may indeed to take another look at the 24-year-old Dutchman in the summer.
But it would appear in the best interests of both player and club if Veldwijk was allowed to stay in Holland for the long-term.