The Toffees reportedly had a £25m bid for the 22-year-old rejected this week, with Wolves adamant that the academy product was part of their plans for the upcoming 2022-23 campaign.
Frank Lampard's side have remained in talks with their fellow Premier League club according to Sky Sports News, despite suffering an initial setback in their pursuit.
The report suggests that the two clubs remain in disagreement over the valuation Gibbs-White, who spent the 2021-22 campaign on loan at Championship outfit Sheffield United.
After several years of being on the fringes of the Wolves first team, and following a six-month loan deal with Swansea City in 2020, Gibbs-White enjoyed a productive campaign of first-team football with the Blades.
The England Under-21s international netted 11 goals and registered nine assists in 35 league appearances in the second tier, leading to an increase in interest in the midfielder's services.
The report suggests that personal terms should not be an issue between Gibbs-White and the Merseyside outfit should a fee be agreed with Wolves, where he has two years remaining on his current contract in the Black Country.