The Merseyside giants have been locked in discussions with Benfica to find an agreement for Nunez, who wants the move to Anfield.
Liverpool are to pay £64m as an initial fee for the Uruguay international, with further add-ons (£12.8m based on Nunez’s appearances and £8.5m based on the club’s success).
The Reds are now putting plans in place to give the player a medical on Monday as they aim to speed through the completion of the deal.
Nunez is currently in Madrid and waiting for the green light to fly to England.
Personal terms have already been agreed and Nunez will sign a six-year contract, running until the summer of 2028.
Liverpool are expected to lose Sadio Mane this summer, with the Senegalese keen to complete a move to Bayern Munich.
Bayern Munich are seeking to agree a fee with Liverpool for Mane, who has been offered a lucrative contract at the Allianz Arena.
