Diaz, 29, left Liverpool for Bayern last summer in a deal reported at around €75m and enjoyed an outstanding debut campaign in Bavaria, scoring 26 goals and providing 23 assists in 51 appearances across all competitions.
L'Équipe reported that the Saudi club have made the winger their top attacking priority this window, with the Colombian said to be open to the move and Al-Hilal reportedly prepared to offer him a net salary in excess of €37m a year. The Saudi side have already brought in Crysencio Summerville from West Ham this summer and are also said to be exploring a deal for Paris Saint-Germain's Ousmane Dembélé.
Despite the scale of Al-Hilal's approach, Bayern Munich have communicated to interested parties that Diaz will not be sold three years before his contract, which runs until 2029, is due to expire. The German champions are said to have identified 20-year-old Arijon Ibrahimovic, recently returned from a loan at relegated Heidenheim, as a potential long-term successor on the wing, though he is not considered ready to inherit such a prominent role immediately.
Bayern have also rejected the idea of letting Michael Olise leave this summer, underlining their reluctance to weaken an attack that helped fire them to last season's title.
Diaz has made 79 appearances for Colombia, scoring 23 goals, and was part of the squad eliminated by Switzerland on penalties in the last 16 of this summer's World Cup.
His importance to Bayern under head coach Vincent Kompany, allied to the gap between Al-Hilal's opening approach and what would be required to draw the German club into talks, means the Bundesliga side are expected to continue resisting interest even if further bids materialise before the window closes.
Al-Hilal are said to have set Bayern a deadline for a definitive response this week as they look to complete their business elsewhere in the market.