With less than a year to run on his contract, Palace chairman Steve Parish has stated Guehi will be sold in the coming weeks unless he performs a U-turn and pens a new deal.
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The Liverpool Echo says the Premier League champions are now making their move.
Liverpool have opened talks with Palace for their club captain and hope to strike terms for a fee in the region of £35m.
Talks between the two clubs are being held first before Liverpool approach Guehi out of respect between the two boards.
The Reds' move could flush out other suitors, which include Newcastle United.