According to reports, the agent of Bruno Fernandes has held “productive” conversations with Al-Hilal.
The Saudi side pushes hard to sign the captain of Manchester United in the coming days.
Fernandes, 30, went to Malaysia on the tour of the Red Devils after the season.
According to transfer expert Ben Jacobs, his agent Miguel Pinho has meanwhile deposited to Saudi Arabia to meet Al-Hilal Chiefs.
Club president Fahad bin Nafel is said to have had positive conversations with Pinho in the Four Seasons Hotel in Riyad.
Al-Hilal will participate in the extensive Club World Cup next month and want to recruit a new superstar to play on time.
It was previously reported that last year's Saudi champions wanted an answer from the Fernandes camp.
The Portuguese midfielder still has to give them a concrete decision.
Man Utd's attitude would be that they want to keep their skipper.
The future of Fernandes could be arranged later this week.
After the last defeat of United's Europa League against Tottenham, Fernandes offered to leave the Red Devils.
The former sporty CP star said: “I have always been honest. I have always said that I will be here until the club tells me it is time to go.
“I would like to do more to be able to bring the club the great days.
“On the day the club thinks I'm too much or it's time to separate, football is that way, you never know. But I have always said it and I keep my word in the same way.
“If the club thinks it's time to separate because they want to come up with some money or whatever, it is what it is and football is sometimes so.”
Boss Ruben Amorim, 40, said earlier this week: “He is really important to us and really important for what we want to build with this team.”