The Colombian is one of the most sought after wingers in Europe this summer.
Diaz has 24 goals and 13 assists in his 98 appearances for the Anfield club so far.
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He has been a hit since arriving from FC Porto in January 2022, but may soon depart.
Per AS in Spain, Barca have been discussing the matter with Diaz's representatives Carlos Van-Strahalen and Raul Pais Da Costa.
Barca's sporting director Deco is said to have met with the duo a few months ago.