Liverpool’s busy summer of signings include Germany playmaker Florian Wirtz from Bayer Leverkusen for a club record £116m plus French forward Hugo Ekitike from Eintracht Frankfurt in a deal worth £79m, pushing their spending past £250m.
Nunez has also been a target for Italian champions Napoli this summer while other European sides have shown an interest.
In January, Liverpool reportedly rejected a bid worth 70m euros (£61m) from Saudi’s Al-Nassr.
Nunez managed just seven goals across all competitions last season, however, he has scored five goals during the club’s four pre-season games, including a hat-trick inside 20 minutes against Stoke in July.
Al-Hilal, who are coached by former Inter Milan boss Simone Inzaghi, finished second in the Saudi Pro League last season.