The Barcelona star shone for his nation against the Soceroos in their opening game of the tournament, scoring one and setting up another in the 3-1 win.
Reds boss Brendan Rodgers was rumoured to have been interested in the South American ace prior to the competition, and it is now understood that scouts from the club were watching him against the Aussies.
His all-action showing is believed to have convinced the Merseysiders of his abilities, with a £27m offer now on the cards.
Reports indicate that Barca are willing to cash in on the 25-year-old as they plot a major summer overhaul, with some rumours suggesting that Juventus are closing in on his signature.
Manchester United are also in the battle, but Liverpool’s Champions League status may well give them the edge.
Rodgers has already signed Rickie Lambert and Emre Can, and is also watching Southampton’s Adam Lallana.