The Dutch shot-stopper is among those Wolves are prepared to part company with this summer.
After slipping into League One, the Molineux-based outfit are looking to trim their wage bill.
New boss Kenny Jackett has informed De Vries that he can leave as a free agent if a suitable offer is put to him.
A return to his native Holland was mooted at one stage, but it appears as though the 32-year-old could now be staying in England.
It is understood that terms have been agreed with Forest and that De Vries is due to undertake a medical at the City Ground on Wednesday.
Should those physical tests uncover no problems, the former Swansea keeper will link up with the Reds for the 2013/14 campaign.
De Vries is vastly experienced when it comes to life in the Football League, having made close to 200 appearances for the Swans, but has found regular football hard to come by during a two-year spell at Wolves.