Even The Athletic writes that the club and player have reached a verbal agreement and that the 26-year-old Uruguayan may join al-Hilal's training camp in Germany.
German Sky Sports journalist Florian Plettenberg also states that Nunez "has given the green light" and that a medical examination is pending shortly.
Liverpool has been linked to Newcastle's Swedish attacking star Alexander Isak in recent weeks and made a bid of 120 million pounds earlier in August that was rejected.
Isak stayed home from Newcastle's preseason tour in Asia and was instructed on Wednesday to train on his own. He did not participate in Newcastle's team meeting for players and families either.