Tottenham Hotspur were previously one of the clubs interested in securing Gordon's signature earlier in the transfer window, but despite a double deal being suggested, Antonio Conte's side instead sealed the £60m purchase of only Richarlison from the Toffees.
Newcastle United are also said to have been interested in acquiring the 21-year-old ahead of the 2022-23 campaign, and have even reportedly had a bid in the region of £35m turned down by the Merseyside outfit.
Following significant attention from elsewhere in the England Under-21s international, Everton have stepped up their efforts to secure Gordon on a long-term contract, according to Football Insider.
The report suggests that Frank Lampard's side have made the new deal a priority for the transfer window, which would extend the winger's stay at the club, whilst also rewarding him with a significant pay rise.
The academy product has come to the attention of many after enjoying a breakthrough campaign in the Premier League last season, during which he scored four goals and registered two assists in 35 league appearances.
Such form helped Everton avoid relegation from the top flight, and after losing Richarlison to Spurs, the likes of Dominic Calvert-Lewin, and Gordon, have also been linked with moves away from Goodison Park during the transfer window.