The 22-year-old has become the subject of interest from Frank Lampard's side following an impressive season-long loan deal with Sheffield United in the Championship during the 2021-22 campaign.
The England Under-21s international netted 11 goals and registered nine assists in 35 league appearances in the second tier for the Blades, after struggling for several years to break into the first team at Molineux.
Gibbs-White is believed to be part of Bruno Lage's plans for Wolves in the upcoming campaign according to Sky Sports News, who report that the offer from the Toffees has been turned down.
The deal, which included potential add-ons, would be only Everton's second signing of the summer were it to be resurrected, following the arrival of James Tarkowski on a free transfer from Burnley.
Following a disappointing 2021-22 campaign in which Everton narrowly avoided relegation from the Premier League, they have already lost Richarlison to Tottenham Hotspur during the transfer window, whilst Dominic Calvert-Lewin and Anthony Gordon are amongst those attracting interest from elsewhere too.
Meanwhile, after breaking into the senior setup at Wolves back in the 2016-17 season, Gibbs-White has gone on to make 86 first-team appearances for the Black Country outfit, but has made just 20 top-flight appearances over the past three campaigns.