Nunez, 22, is set to break Liverpool's transfer record, with the deal expected to be worth around €80 million plus €20m in add-ons. The agreement between the clubs has yet to be completed, but talks are progressing well.
Benfica were initially only willing to negotiate Nunez's departure for around €130m.
The Uruguay forward, who joined Benfica from Almeria in the summer of 2020 for €24m, is under contract through June 2025 and has a €150m release clause.
Almeria will receive 20% of any profit from Nunez's transfer.
Nunez attracted the attention of top European clubs after an impressive 2021-22 season in which he scored 34 goals in 41 appearances for Benfica.
Nunez was the top scorer in Portugal's top flight this past season with 26 goals.
ESPN reported on Thursday that United have prioritised the signing of a central midfielder rather than engaging in a battle with Liverpool for Nunez.
Liverpool coach Jurgen Klopp had praised Nunez after his team's Champions League quarterfinal encounter against Benfica, saying that Nunez is "really good and has a big career ahead of him."
Nunez, who is on international duty with Uruguay, has remained tight-lipped about his future, but chose his strike at Liverpool on April 13 as the best goal of his career.