The 28-year-old returned to the Premier League with Palace in the summer of 2024, and was crucial in the club's run to the UEFA Conference League title last season, with 21 goals scored in all competitions.
Liverpool have been linked with several attacking targets over the summer as Andoni Iraola looks to replace Mohamed Salah.
The Reds are now on the verge of landing a prolonged transfer deal for PSG winger Bradley Barcola and that has reduced their need for Senegal star Sarr.
Sarr is under contract at Selhurst Park until 2029, and new boss Pierre Sage has openly confirmed his desire to him, and as per the latest from The Athletic, Liverpool will not follow up their previous link.
The Reds have been informed it would take an 'astronomical fee' to persuade Palace to sell and the Merseyside giants will not pay more for Sarr than the £100M up front outlay on Barcola.