SunSport revealed the forward is a shock candidate to join the Spanish giants this summer.
He has also deleted all pictures of himself playing for Liverpool from his Instagram page.
Nunez has now appeared to fuel the speculation after linking up with an international team-mate.
The 24-year-old is in Barcelona with fellow Uruguayan Ronald Araujo, who plays for Barca.
Araujo shared a selfie of himself and Nunez to Instagram along with the words: “Mi Hermano,” meaning “My Brother”.
The pair have played together 17 times for Uruguay at both youth and senior level.
It comes as Barcelona eye a potential move for the striker in the summer.
Nunez has been identified as a possible replacement for Robert Lewandowski if he leaves the club.
Barca also believe Liverpool would be willing to sell Nunez to boost incoming boss Arne Slot’s transfer kitty.
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Klopp has botched his Liverpool exit… and it’s cost him his legacy, says Dave Kidd
By Dave Kidd
NOW we know Jurgen Klopp’s final major trophy haul at Liverpool — one Champions League, one Premier League, one FA Cup, two League Cups and (if you must) a World Club Cup.
But where does his reign stand among the greatest of the Premier League era?
In black-and-white terms, Klopp is way behind Sir Alex Ferguson and Pep Guardiola, the only two men to have won multiple Premier Leagues and a Champions League at the same club.
Those two sit alongside Brian Clough, Bob Paisley and Sir Matt Busby as the undoubted all-time managerial greats of the English game.
But Klopp ranks in the next tier down — with Arsene Wenger, Jose Mourinho (the Chelsea version), Bill Shankly and Don Revie.
These were all men with the strength of character to transform their clubs in their own image and enjoy success but who did not win as much as they might have done.
Had Klopp managed to keep his intentions under wraps and ended up with another title, perhaps even a treble or quadruple, he’d have edged himself up into that highest echelon with Ferguson, Guardiola, Clough, Paisley and Busby.
But deciding the timing and the manner of your exit is one of the toughest calls for any manager or sportsman.
Klopp got it wrong.
Read Dave Kidd’s take on Klopp’s demise in full here.
Or click here to check out all of Dave Kidd’s articles.
The rumours have been fuelled further by the Reds star’s social media activity.
Any Liverpool-related photos have been removed from Nunez’s Instagram, leaving snaps of him at Benfica and Uruguay or enjoying family time.
Nunez still has four years remaining on his contract at Anfield, having signed from Benfica in 2022.
Despite criticism from rival fans, he has scored 18 goals and provided 13 assists across all competitions this season.
Only Mohamed Salah has scored more goals than Nunez for Liverpool so far this term.