The 21-year-old has been the subject of interest from Newcastle in this transfer window and missed the squad’s return to the Finch Farm training complex on Tuesday following the sacking of manager Frank Lampard.
Everton again expected Gordon to be at training on Wednesday but the PA news agency understands the academy graduate was absent for a second day without permission, casting further doubt over his long-term future at his boyhood club.
Midfielder Amadou Onana, reportedly attracting interest from Arsenal, did rejoin the group on Wednesday having been given an authorised absence by the club the previous day.
Only a month ago, Gordon, whose current contract expires in 2025, was set to sign a new deal but things appear to have soured since then.
Having started the Boxing Day defeat to Wolves, the winger has since made just two substitute appearances totalling 30 minutes and, despite being the club’s joint-top scorer in the Premier League this season with three goals, he was left on the bench for the entire 90 minutes in last weekend’s defeat against West Ham.
Both Newcastle and Chelsea made offers for Gordon in the summer but the club were adamant the youngster was not for sale and, while that resolve may now be weakening, without a manager in place it makes sanctioning any potential departure difficult.
It is an added complication relegation-threatened Everton do not need right now as they search for an eighth permanent manager in just under seven years of owner Farhad Moshiri’s reign.
Nine defeats in 12 league matches accounted for Lampard with the club only staying off the bottom of the table on goal difference.
Former Leeds boss Marcelo Bielsa emerged as the favourite to replace him but a deal for him remains complicated and, with the transfer window closing in six days, Everton want the new man in place by the end of the week.
The club have also considered Carlos Corberan, who has done an impressive job turning around West Brom’s failing fortunes in the Sky Bet Championship.
The out-of-work ex-Burnley boss Sean Dyche and Sam Allardyce, who had a previous six-month spell at the club to save them from trouble in the 2017-18 season, have also been mentioned.
Moshiri admits this is now a pivotal time for the club, which have not been relegated since 1951.
“This is the most critical time in our history. It is almost an existential point,” he said in an interview with the Everton Fan Advisory Board, conducted before Saturday’s West Ham game.
“I have faith in this board. I’m not shy to make changes. We make changes when there is a need.
“We will be ruthless. We need to be calm and we need to go beyond our current position on the pitch.”
A chaotic 24 hours on Tuesday also saw Everton miss out on the loan signing of Villarreal winger Arnaut Danjuma as, despite an agreement being in place, Tottenham hijacked the move and confirmed the Dutch forward as their player on Wednesday.
That means a squad which is in desperate need of refreshing is still without a new face in January.
Moshiri admits failings behind the scenes have contributed to a scattergun and largely unsuccessful transfer policy under his ownership.
“Why hasn’t it worked? I think that is a big question as the structure is there,” he said of the move to a director of football during his time at the club.
“We have had Steve Walsh from Leicester, a very experienced scout, Marcel Brands, one of the top European directors, and now Kevin Thelwell.
“I think the reasons are that some of the deficiencies in various departments of football management were not addressed.
“Those are imperative to proper recruitment, that affects the performance availability and Financial Fair Play. Once you buy these players, you cannot buy additional players.
“We got very little out of these players.”