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.
The Reds have also sold Colombia winger Luis Diaz to Bayern Munich for £65.5m and midfielder Tyler Morton to Lyon for £15m, while England Under-21 midfielder Harvey Elliott could also leave the club.
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.
The Saudi side features former Wolves midfielder Ruben Neves, ex-Manchester City full-back Joao Cancelo and former Fulham and Newcastle striker Aleksandar Mitrovic, as well as Senegal centre-back Kalidou Koulibaly and Morocco goalkeeper Yassine Bounou.
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