The BBC reported that the 25-year-old will undergo a medical examination on Friday as Spurs intensify their efforts in the transfer market.
Additionally, a £55 million agreement has reportedly been reached with West Ham for winger Mohammed Kudus.
Gibbs-White was previously associated with Manchester City after playing a crucial role in Forest's seventh-place finish in the Premier League last season.
He netted seven goals and provided 10 assists in 34 Premier League appearances, earning senior England recognition under both Lee Carsley and Thomas Tuchel.
His exit marks the second significant loss for Forest in just a few days, as Anthony Elanga is set to move to Newcastle in a £55 million transfer.
Gibbs-White joined Forest from Wolves in 2022 for an initial £25 million, which could increase to £42.5 million with add-ons.
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