Sam Allardyce has less than 24 hours now to further strengthen his backline.
The Eagles signed left-back Patrick van Aanholt from Sunderland today for a fee of £14million.
And a move for Sakho is now being lined up, according to Sky Sports, but there are sticking points over a switch.
Jurgen Klopp is keen to offload the 26-year-old France international on a permanent basis.
Mamadou Sakho has appeared for Liverpool's Under-23s this season but not the first team
Liverpool are holding firm on their £20m valuation of Sakho
The Reds are not looking to send Sakho out on loan, and that will make him an expensive acquisition for Palace.
Allardyce is looking to boost his side's chances of Premier League survival this season, with Palace sitting in 18th place.
However, Liverpool are holding firm on their £20m valuation of Sakho, despite not making a first-team appearance since April.
The centre-half has fallen out with Klopp, but the manager does not want to sell him on the cheap.
Liverpool transfers: Deadline day rumours rated
Mon, January 30, 2017
Football Whispers have rated Liverpool's chances in the transfer market ahead of deadline day (1 – unlikely, 5 – likely)
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Football Whispers have rated Liverpool's chances in the transfer market
With Palace set to land Olympiakos midfielder Luka Milivojevic tomorrow for £12.5m, they will hope to reach an agreement over Sakho's fee.
Meanwhile, his wages are also an issue, with Sakho reportedly still on £100,000 a week at Anfield.
Southampton have also shown interest during January, but Palace are attempting to land him.