Forest are understood to be looking into whether the player's confidentiality agreement - related to a £60m release clause - was breached.
It was widely reported Gibbs-White was set to have a medical with the north London club on Friday after they had triggered the release clause, but this was cancelled after Forest insisted they had not given permission for the move to take place.
Under Premier League rules clubs are not allowed to talk to players under contract unless they have been granted permission.
Forest are reportedly furious with Tottenham and are willing to go to whatever lengths necessary to prevent the transfer with Gibbs-White's teammate Anthony Elanga set to join Newcastle for £55m.
Gibbs-White joined Forest from Wolves for £45.5m in August 2022.
He has made 118 appearances for the club, scoring 18 goals and 28 assists.