The 13-time Saudi Arabian champions are currently top of the Pro League, however there is a general dissatisfaction with the technical level of the team who are coached by German Thomas Doll.
Al Hilal chairman Abdulrahman bin Musa'ad told reporters this week that he would cancel Doll's contract if he could find a suitable replacement for him.
Aguirre hasn't travelled to Saudi Arabia for negotiations with the club, however it is understood Al Hilal have opened discussions and are waiting on the former Mexico boss' response.
The 53-year-old Mexican was sacked by Zaragoza in late December with the club languishing down the bottom of the Spanish Liga table.
Aguirre has previously coached the Mexico national team along with Spanish clubs Atletico Madrid, Osasuna and Zaragoza.
In other news, Al Hilal are believed to be willing to sell Cameroon international Achille Emana, who only joined the club midway through last year from Real Betis.
Al Hilal will listen to offers from France and Turkey for the 29-year-old attacking midfielder's signature.
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