The London club were said to have real interest in the Toffees youngster.
However, Sky Sports claims their interest has cooled, as they will merely monitor his progress for now.
Spurs are very close to signing Richarlison from Everton.
According to several sources in England, the Brazilian forward is likely to officially sign for the club this week.
For his part, Gordon is happy to stay with Everton, where he believes he can get plenty of first team football next season.