Gordon, 21, was one of several members of the squad to have been given time off on Tuesday, but sources have said that the England under-21 international had been due to return to training on Wednesday and failed to do so. Gordon was also absent from Everton's Finch Farm training complex on Thursday.
Newcastle have made an initial enquiry about signing the player this month, but sources have said the club will not meet Everton's £60 million asking fee for the transfer of the highly-rated forward.
Everton rejected two offers of £40m and £45m from Chelsea for Gordon last August, but the player has endured a difficult season at Goodison Park, scoring just 3 goals in 18 appearances for the club.
He was subject of intense criticism from Everton supporters on social media following the 2-1 home defeat to relegation rivals Southampton earlier this month after being accused of laughing at fans who were protesting outside Goodison Park.
Sources have said that Everton and Newcastle are in talks over Gordon, with Chelsea considering a renewed move for the Liverpool-born player who joined Everton when he was 11-years-old.