El Mundo Deportivo says the 21 year-old has impressed Barca scouts and 'aced' his audition against the champions-elect last week.
Barca will continue their watching brief in the coming games with the view to recommending his signing to the football chief Pep Segura ahead of the summer market.
Segura is seeking a young centre-half signing, with Ajax's Matthijs de Ligt also under consideration.
Nunez's current deal carries a €30m buyout clause.
Need a VPN? Or seeking to switch? Then support Tribal Football by clicking here to sign up with our official partners NordVPN. Not only will you receive the best VPN experience, but also great discounts by signing up via Tribal Football. Thanks for your support!