Gibbs-White has met with Forest's management to discuss his future, and it is understood that he has expressed his desire to have his next season's destination clarified.
Forest staff have reportedly been impressed by Gibbs-White's commitment during preseason training this week, despite his recent transfer speculation.
The midfielder, who has represented England, wants his future settled before the Forest squad travels to Portugal for a training camp this weekend.
It is suggested that Forest may reconsider their stance if Tottenham return with a higher offer of £65m for Gibbs-White's services.