The centre-forward is back in England this week with Uruguay for their friendly against the Three Lions.
Advertisement
Advertisement
Asked about the Liverpool support, Nunez said: "The truth is they made me feel really welcome and my family too.
"I went through a difficult time personally, but the fans always gave me support and affection, and that for me was very important.
"And obviously being back here, I do miss them."
Nunez has been linked with a return to England after a difficult time in Saudi Arabia, with Newcastle mentioned as a potential suitor.