Palace have said in the past that Sakho is out of their price range, but following an alarming start to the Premier League season, they are doing all they can to agree a deal.
Reports claim that Eagles chairman Steve Parish has offered the Reds £22million plus £3million in add-ons.
That means there remains a substantial gap between what Palace are willing to pay and the price the Reds have placed on the France international, who spent the second half of last season on loan at Selhurst Park.
West Brom and Leicester are also keen on the 27-year-old centre-back, who fell out of favour with Liverpool manager Jurgen Klopp last summer after a number of indiscretions.
Now it remains to be seen whether they, or Palace, can agree a fee for Sakho before the transfer window closes on Thursday, and it could go right to the wire.