Al-Hilal are said to be preparing an annual salary offer worth around €25 million in an attempt to persuade Díaz to make the move, nearly double his reported €14 million-a-year deal in Munich.
The Saudi club have not yet opened talks with Bayern themselves, with the plan being to first secure the player's agreement before approaching the German champions with a fee reported to be in the region of €120-150 million.
Notably, the negotiations with Díaz's camp are said to be led by Richard Hughes, Liverpool's current sporting director, who is expected to join Al-Hilal once the European transfer window closes and already appears to be taking on responsibilities for his prospective new club.
Hughes has a prior relationship with Díaz from his time at Liverpool, where the winger played before his move to Bayern last summer.
Díaz has enjoyed an outstanding debut season in Munich since arriving from Liverpool for around €70 million, scoring 26 goals and providing 23 assists in 51 appearances across all competitions and establishing himself as a key figure under Vincent Kompany.
He remains under contract at the Allianz Arena until 2029, giving Bayern a strong negotiating position should Al-Hilal formally approach the club, and there has been no indication so far that Bayern would be willing to sanction a sale of one of their most important attacking players regardless of the fee on offer.
The interest in Díaz comes as part of a wider spending spree by Al-Hilal, who recently completed the signing of Netherlands international Crysencio Summerville from West Ham United in a deal worth around €76 million.
The Saudi club, who have a total transfer budget reported to be as high as €350 million this summer, have also been credited with interest in other high-profile attackers, including Chelsea's Pedro Neto and PSG's Ousmane Dembélé, as they continue to pursue some of Europe's most sought-after forwards regardless of their contractual situations.