The 24-year-old striker, who was born in the Netherlands but qualifies to play for South Africa and has publicly said he would like to don the jersey, enjoyed a successful loan spell at PEC Zwolle last season in which he scored 14 goals in 36 starts.
He had said previously he had no intention of returning to England to play for Forest and rather wanted to move permanently to the Netherlands or China, but has since changed his mind.
The English club have a new manager in Frenchman Philippe Montanier, which means a clean slate for Veldwijk.
And Forest teammate Chris Cohen has been full of praise for Veldwijk in the early part of pre-season.
“Lars scored a lot of goals in Holland and has interest in him from other sides. He looks fit and strong," said Cohen.