As revealed exclusively by Goal.com UK early on Thursday, the Merseyside club were preparing to make a final offer for the Uruguayan after having an initial offer of £12.7 million rejected by the Amsterdam club.
And now, Voetbal International reports the two clubs are still far from agreement regarding a price for the striker after Liverpool made another offer.
Ajax are understood to be holding out for at least £21m for Suarez, though they had previously set an asking price of £30m.
Manager Frank de Boer has indicated that Liverpool have until Saturday to agree a fee with the Dutch club for the World Cup star, who is believed to want a move to Anfield.
Liverpool may now be forced to wait until the summer to move for the player.