Palace see Diomande as a replacement for Marc Guehi and had him on standby in the event the club captain was to leave over the summer.
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Ultimately, Palace blocked Guehi's move to Liverpool on deadline day, though are still keen on Diomande.
Transfer expert Sacha Tavolieri is reporting: "Liverpool in pole position for Marc Guéhi, Crystal Palace targeting Ousmane Diomandé to replace him."
Diomande, 21, has been with Sporting for the past two years after originally being snapped up from FC Midtjylland.