ESPN reported on Friday that both clubs were in advanced talks over a deal, and sources confirmed that Liverpool are set to break their transfer record to sign the striker.
According to ESPN sources, Nunez will sign a five-year contract at Anfield, and he has left the Uruguay national team to travel to England to undergo a medical.
Sources have told ESPN that an agreement was reached on Saturday between the two clubs worth €75 million, plus €25 million in add-ons.
According to ESPN sources, Nunez is keen for regular Champions League football, which put Liverpool ahead in the race to sign him.
The incoming deal could have an impact on the future of Sadio Mane, who has attracted interest from Bayern Munich, with Liverpool turning down two offers from the Bundesliga champions for the forward.
Nunez, who joined Benfica in September 2020, was the top scorer in Portugal's top flight last season and added some stellar performances in the Champions League, ending the year with 34 goals in 41 appearances.
The striker began his career at Uruguayan side Penarol before moving to Spanish second-division side Almeria in 2019, where he scored 16 goals in 32 games. Almeria will receive 20% of the profit from Nunez's transfer.
Liverpool boss Jurgen Klopp praised Nunez after his team's Champions League quarterfinal clash against Benfica in April, saying that Nunez is "really good and has a big career ahead of him."