Gray, 27, seemed to criticise manager Sean Dyche on social media in the wake of a failed switch to fellow Premier League side Fulham.
Dyche responded by reminding Gray that no moves away are sanctioned without the club having the final say.
The transfer window in Saudi closes on Thursday.
Gray is yet to play for Everton this season and has also been linked with a move to Turkish side Besiktas.
The Jamaica international has scored nine goals in 67 Premier League appearances since arriving at Goodison in 2021 after a brief spell with Bayer Leverkusen followed six seasons at Leicester City.