The 29-year-old has spent roughly three seasons at the Hawthorns.
But with opportunities limited in the Premier League, Hegazi has decided it is time to move on, according to Sky Sports.
The centre-back will sign on loan for the Saudi Premier League club, with a view to a permanent deal.
Hegazi played 38 league games in his first two seasons for the club, but has become a peripheral figure since Slaven Bilic took over last term.
He played 16 games last season during their promotional campaign, and only one Premier League game this season.