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Although the club are open to a sale, the offer would reputedly need to be right for the board to seriously consider it.
Although Liverpool are yet to make contact with Palace, discussions are expected to 'begin soon'.
Italian giants Inter Milan were reportedly among the interested clubs but are said to have since placed their interest on the back burner.
Elsewhere, Fabrizio Romano claims that a medical for Milos Kerkez has been booked for next Tuesday following a 'technical issue'.
Speaking on his YouTube channel, the Italian said: "After resolving a technical issue, Liverpool and Bournemouth decided to proceed with the formal steps, so exchanging documents, exchanging emails
"Milos Kerkez to Liverpool is a here we go, £40m - that's the price for the player
A five-year contract is ready for the Hungarian left-back.
"One more piece of information for Liverpool fans, Tuesday next week should be, from what I understand, the day for Milos Kerkez to travel to Liverpool for medical test and contract signing, so it's all set
"The player only wanted to join Liverpool, I can tell you that the player was in the list of several clubs around Europe, considering a move for him, even while Liverpool were not closing officially this deal in the recent weeks, they tried to enter, but there was never a possibility, because Kerkez only wanted to go to Liverpool, and now we can consider Kerkez as a new Liverpool player."