Hegazi joined the Saudi Arabian side in October 2020 with the defender initially making the move on loan.
But the deal included an obligation for a permanent transfer which has now been completed, with reports suggesting Al-Ittihad agreed to pay £2.5million to sign the Egyptian.
It is not known how much of that fee Albion still feel they are owed.
But cash-rich Al-Ittihad have disputed what is left to pay – with Albion turning to FIFA for a resolution.
Hegazi was Albion's top earner when he left The Hawthorns with the club eager to clear his £70,000 a week salary from their wage bill.
He received a further pay rise following his move to the Middle East.
And he has since gone on to impress for Al-Ittihad Jeddah – making 37 appearances for the club, in which he scored six goals, including three in nine games this season.
Albion hope to receive an answer from FIFA this week.
If the governing body rules in their favour, they could receive funds to boost Valerien Ismael's transfer kitty in January.
As well as the money for Hegazi, Albion still haven't received a penny for Nathan Ferguson following his move to Crystal Palace.
After running down his contract at The Hawthorns, Ferguson signed a three-year deal with Palace in July 2020.
As he is under 24-years-old, Albion are entitled to compensation for the England youth international.
And they are expecting that compensation fee to be substantial after they agreed to sell Ferguson to Palace for an initial £11million just six months earlier.
That transfer broke down after the defender failed his medical due to a problem with his knee – with the full-back then going on to complete his move one his Baggies contract expired.
Since then, though, a series, of injuries have denied Ferguson a single minute in a Palace shirt – with an Achilles injury currently keeping him sidelined.
But despite Ferguson having been with the Eagles for over a year, the Express & Star has been told a tribunal to determine his fee still hasn't taken place.
The coronavirus pandemic is understood to be one reason for the delay.
Another is that Palace have made bids to buy Ferguson in a bid to prevent the fee being decided by a tribunal. But those offers have been rejected by the Baggies.