The Sun says Barca see Nunez as a potential replacement for Robert Lewandowski.
And the Catalans believe Liverpool will sell with the need to raise funds to help incoming manager Arne Slot strengthen his squad next season.
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Nunez, a 100m signing two years ago, has struggled to live up to his price-tag.
And sources in South America state the Uruguay striker is keen on the chance of pulling on the Barca shirt.