The 30-year-old has not played a single minute of competitive action this season, and has not been in a matchday squad since the Toffee's season opener versus Fulham.
Manager Sean Dyche has said Gomes is currently absent with a calf injury, but has not given any timeframe on when he could return.
Therefore, Football Insider claims that Everton are planning to let the player leave in 2024, with his contract set to expire next summer.
Gomes has not featured since being taken off at half-time with Everton 2-0 down to Crystal Palace at home in the penultimate game of the 2021-22 Premier League campaign.
Everton went on to win 3-2 to seal top-flight survival under Frank Lampard, but Gomes was not in the manager's plans the following season.
That was his 100th appearance in an Everton shirt after joining from Barcelona permanently in 2019 after an impressive loan spell at Goodison Park the season prior.
Having not convinced Lampard though, the Euro 2016 winner was then sent on loan to Lille in Ligue 1 and featured regularly for Les Dogues as they achieved European qualification last season.
Despite a relatively successful spell in northern France, Lille opted not to make the deal permanent this summer, with Gomes' £120,000-per-week salary believed to be a stumbling block.
The midfielder has struggled to ever reach the same levels since breaking his leg in a freak collision against Tottenham Hotspur back in 2019.
Gomes would go on to miss most of that season, returning after the COVID-enforced break in 2020, but he never regained a regular spot in Everton's midfield.
The arrivals of Abdoulaye Doucoure and Allan under Carlo Ancelotti pushed Gomes down the pecking order, and signings of Amadou Onana and James Garner last summer meant there was no place for him in the club's plans.
Despite a current shortage of midfield options at the club, even if Gomes returns from his current injury, it is unlikely he would get much game time in a blue shirt.