The Daily Mail says PSG is showing interest in the Colombia international.
However, the 27-year-old has a contract until the summer of 2027 and has stated he is happy in Liverpool.
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PSG still plan to present a bumper offer, but Liverpool would prefer not to sell the player.
Colombian media sources have also reported that Barcelona met Daz's agent and expressed their interest last week.
According to the source, Liverpool want between 120-140m to sell Daz.
Daz has scored eleven goals and five assists in 38 competitive games this season.