Nunez scored 34 times in all competitions for Benfica last season and is rated at €100m (£85.5m); He wants to move to Liverpool and is ready to sign five-year contract;
Manchester United are also interested in the 22-year-old
Liverpool's director of football, Julian Ward, is in Portugal to try to complete the transfer, with negotiations centred on the structure of the deal.
Benfica are asking for at least €100m (£85.5m) but Liverpool are only willing to pay a total they consider fair value.
The Uruguay international scored 34 times for Benfica last season in all competitions, including goals in both legs of the club's Champions League quarter-final defeat to Liverpool in April.
Manchester United are also admirers of the 22-year-
"Darwin Nunez was one of the best players this season in the Portuguese league by far. The other one was Luis Diaz who moved to Liverpool in January and that made Nunez the absolute best
"Benfica finished the season in third place and failed to get a direct spot in the Champions League but in 41 games, Nunez scored 34 goals and registered four assists - so you're talking about one of the best strikers.
"He's a 'modern football striker' - like Erling Haaland and Kylian Mbappe - strikers who don't just focus on scoring goals. They focus on playing for the team and making the whole team play well. That's why we're talking about €100m.
"When you talk about a player like Darwin Nunez, you think about a typical number nine that plays inside the penalty area. But he can easily play out wide to break spaces for other players in the central areas if teams need him. It's a very good deal for Liverpool, who already used the Portuguese league with Luis Diaz in a massive transfer for Liverpool which the winger completely deserved.
"In Jurgen Klopp's hands, Darwin can be of the top strikers in the world. Nowadays, he's not one of the top strikers because he doesn't play in the top five leagues. We have to see how he develops in the Premier League, which is one of the best leagues in the world."