The 22-year-old starred for his Portuguese club during the 2021-22 campaign, scoring 34 goals and registering four assists in 41 appearances in all competitions.
Manchester United have been strongly linked with the Uruguay international over the last few weeks, but Liverpool have recently moved to the head of the queue for the centre-forward.
According to Italian journalist Fabrizio Romano, following a meeting in Portugal between the two parties, a deal has now been agreed, and Nunez will travel to England on Monday to undergo a medical.
Romano claims that the South American will pen a six-year contract with the FA Cup and EFL Cup holders, taking him until the summer of 2028.
Liverpool will allegedly pay an €80m (£68.3m) fee plus €20m (£17m) in add-ons, with the Merseyside giants moving quickly to agree a deal amid competition from a number of other clubs.
Nunez found the back of the net on 26 occasions in 28 league appearances for Benfica during the 2021-22 campaign, while he also netted six times in 10 Champions League outings.
Two of the forward's six European goals last term came against Liverpool in the quarter-finals of the Champions League, registering home and away versus Jurgen Klopp's side.
Nunez will allegedly now fly from Spain to England alongside his agent, so an announcement from the Reds could arrive early next week.
There is also uncertainty surrounding the future of Mohamed Salah, with the Egypt international's current deal at Anfield due to expire next June.
Nunez will arrive at Anfield off the back of scoring 47 goals and registering 16 assists in 84 appearances for Benfica, joining the Portuguese outfit from Almeria in September 2020.
The forward was left out of Uruguay's clash with Panama on Saturday evening, fuelling suggestions that he was on the verge of securing a move to last season's Champions League finalists.