Al Hilal are willing to make Bruno Fernandes one of the best-paid players in the world and pay £100m to sign the Manchester United captain.
Fernandes' agent Miguel Pinho has been in Riyadh for talks with senior Al Hilal executives.
Saudi Pro-League insiders believe it is a positive sign for Al Hilal that Pinho has travelled to Saudi Arabia.
Al Hilal are willing to almost treble Fernandes' £250,000-a-week wages at Old Trafford.
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It is up to the player now to decide what he wants to do and he may speak after United's game in Hong Kong on Friday.
United want to keep Fernandes, but Al Hilal believe every player has a price - especially one who will be 31 in September.
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The Portugal international signed a contract extension last summer until 2027 with the option of a further 12 months.
Al Hilal have also held talks about signing Cristiano Ronaldo, who will become a free agent next month if he does not sign a new contract at Al Nassr.
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Ruben Amorim hails Bruno Fernandes captaincy at Manchester Utd
Manchester United head coach Ruben Amorim hails captain Bruno Fernandes' leadership qualities at the club and says they are vital for what he wants to achieve going into next season
Al Hilal expect to have at least one big-name signing and a new head coach when they play in the Club World Cup in the United States in June.
Inter Milan manager Simone Inzaghi is expected to be appointed the club's head coach after Saturday night's Champions League final against Paris Saint-Germain.
Follow the transfer window on Sky Sports
The first of two summer transfer windows is upon us - and there is no better place than Sky Sports to get all the latest transfer news and rumours.
Use the Sky Sports app and website for all your updates in our dedicated Transfer Centre and Premier League club blogs, plus live Q&As with our reporters throughout the summer.
The Transfer Show returns to Sky Sports News from Sunday June 1 for the start of the pre-Club World Cup window and will then be on every weeknight at 5pm and 7pm until the deadline on Tuesday June 10.
The summer transfer window will open again on Monday June 16 until Monday September 1 - with the deadline brought forward to 7pm this year