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.
The Senegal international now has over 100 Premier League games under his belt - across spells at Watford and Palace - and could offer Andoni Iraola a vital squad boost.
Liverpool have been frustrated in their pursuit of several attacking targets this summer as part of Iraola's push for replace Mohamed Salah on the right-side of his forward line.
The Reds are still locked in transfer talks with PSG over Bradley Barcola - and Sarr's Senegal teammate Ibrahim Mbaye - but a Fabrizio Romano exclusive claims a £50M offer could now be incoming on fresh target Sarr.
Yankuba Minth looks set to stay at Brighton, and despite Palace reportedly rejecting two offers on Sarr from Galatasaray, a move to Anfeld for Champions League football could catch his eye.
He's under contract at Selhurst Park until 2029, and new boss Pierre Sage has openly confirmed his desire to him, and that could increase the club's valuation in the coming days.