The Brazilian has arguably been the Baggies best player since arriving – initially on loan – from Sporting Lisbon in August 2019.
After shining in the Championship, Pereira also impressed in the Premier League with a brace in a 3-2 win over Wolves amongst his Albion highlights.
But the 25-year-old told the club he wanted to leave following their relegation from the top flight.
And his departure turned into a public spat earlier this week.
Speaking after the friendly win over Birmingham, boss Valerien Ismael said he wasn't considering Pereira for selection because he isn't "committed" to the club.
In a statement, the forward responded by saying he felt that comment was disrespectful, while he also revealed he had received a life changing offer to leave.
That offer came from Saudi side Al Hilal with the two clubs having been working to agree a transfer fee for a number of weeks.
And it is understood an agreement is now close to being reached with Pereira having been given approval to undertake a medical with the Pro League side.
According to reports, that medical will take place in Paris before Pereira will then fly to Saudi Arabia where he is expected to earn in excess of £100,000 a week.