Gordon was the subject of interest from both Chelsea and Newcastle this summer, but a move failed to materialise as the Toffees held firm on their refusal to sanction a sale after a difficult season.
The Magpies consider Leicester City’s James Maddison a much more achievable target as they look to bolster their ranks in attacking midfield in January.
Newcastle still hold an interest in prising Gordon away from Everton but feel that their chances of pulling that off in January are poor.
The Magpies feel they have a better chance of landing Maddison, who was the subject of a rejected £40m bid from them earlier in the summer.
Maddison was thought to be keen on the move but Leicester’s £60m valuation was one that Newcastle were not prepared to meet.
Newcastle look set to try again for him in January, with Everton remaining determined that Gordon should not leave Goodison Park.
The Magpies are currently placed eleventh in the Premier League table and will travel to London Stadium to take on West Ham on Sunday.