The Colombia attacker has been linked with PSG and Atletico Madrid in recent weeks, with his father even talking up a move to Atleti.
However, Colombian reporter Pipe Sierra states the Reds aim to convince Diaz about staying with a pay-rise proposal.
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Diaz's current deal runs to 2027.
This season, the 27 year-old midfielder has played 43 matches for the team, scored 13 goals and made 4 assists.