The forward has attracted interest from a number of clubs including Manchester United after scoring 34 goals in 41 appearances for Benfica in the 2021-22 season.
A previous report stated that the Red Devils were closing in on a deal for the 22-year-old, who found the net on six occasions in 10 Champions League games last term.
There were also reports suggesting that midfielder Andreas Pereira could be used in a potential transfer by Erik ten Hag's side.
However, according to Football Insider, Liverpool are set to make a formal approach for the Uruguayan, challenging their Premier League rivals for his signature.
Nunez is believed to suit the profile of a Jurgen Klopp player, while the report states that the Benfica forward is "keen" on a move to Anfield.
With three years still left to run on his current contract, Liverpool may have to pay a fee in the region of £55m to prise Nunez away from the Portuguese club.
Since arriving from Almeria in 2020, Nunez has scored 47 goals in 84 appearances for Benfica, including a goal in each leg of their Champions League quarter final tie against Liverpool last season.
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