The Colombia international attracted interest from Everton over the summer, but Porto were said to have recently revised their demands, potentially pricing Rafael Benitez's side out of an approach.
Such news saw Barcelona move into pole position for his signature, after they enquired about the 24-year-old but they may now face intense competition.
According to The Independent, Liverpool have now joined the La Liga giants in the race for Luis Diaz's signature, with Jurgen Klopp said to be keen to add to his attacking ranks.
The Colombian has kicked off the new campaign with five goals and an assist from the opening seven Primeira Liga outings, after starring for his nation at this summer's Copa America with four goals in five games.
The Reds had a chance to take a closer look at their reported target when they took on Porto in the Champions League group stage on Tuesday, and the 24-year-old started on the left-hand side as Klopp's men picked up a rampant 5-1 win at the Estadio do Dragao.
CSKA Moscow 
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