The 22-year-old would become Forest's 16th signing of a busy summer at the City Ground.
Forest have spent most of the summer trying to sign Gibbs-White, who came through Wolves' academy.
The Stafford-born player has started both Premier League games for Bruno Lage's side this season.
However, Wolves are still trying to reshape Lage's squad and it was likely Forest would make another push to sign him.
Forest will pay an initial fee of £25m, plus up to £17m in potential add-ons.