It is reported by Voetbal Zone that the club, who finished 6th in Eredivisie last term and won the Dutch Cup in 2014 with a 5-1 win over Ajax in the final. They made it to the Dutch Cup final again last season, but lost to Groningen in the final.
They are now hoping to push on and break the monopoly at the top of Dutch football, with Veldwijk seemingly a man they want to help them on their crusade.
Despite scoring 31 goals in 41 games for Excelsior in 2013-14 the striker has struggled in English football. He has not scored for Forest in just 14 appearances and has hardly convinced when given the chance.
He has recently been linked with a move to fellow Championship side Brentford.
Brentford parted ways with Mark Warburton this summer, despite his excellent season in charge at Griffin Park. They replaced him with Dutchman Marinus Dijkhuizen.
The 43-year-old arrived from his job at Excelsior Rotterdam, where he worked with Veldwijk.
However, he confirmed last week to Get West London that he was not keen on the player.
Nottingham Forest are reluctant to let many players go, because of their current transfer embargo, but if Zwolle make a good offer for the player, he is likely to return to The Netherlands in the coming weeks.