Correio da Manhã says Liverpool have "shown the most desire" to sign Diaz.
The Colombian winger has impressed for the Portuguese giants this season and has been linked with teams from across Europe including Premier League rivals Manchester United and Chelsea.
But Liverpool are actually "those who have shown the most desire to count on the player".
It adds that the player's performances in this season's Champions League show he's "ready for new flights" and report he could be on his way to Anfield.
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