No offer has been made for the 28-year-old Senegal international as things stand. Liverpool's interest emerged after their pursuit of Brighton's Yankuba Minteh stalled, with the Gambia international valued at £80m against an initial Liverpool expectation of around £50m.
Talks are continuing for Paris Saint-Germain's Bradley Barcola, who remains a separate and higher priority for the left wing, while the Sarr situation is being explored as one of several back-up options rather than a fixed plan.
Sarr is an older profile than Liverpool have typically pursued in recent windows, but he arrives with a proven Premier League track record, having scored 21 goals in all competitions last season as Palace won the Europa Conference League.
He returned to English football via Palace from Marseille in August 2024, following an earlier spell at Watford, and has quickly become one of the club's most productive attackers alongside Michael Olise, Eberechi Eze and Jean-Philippe Mateta.
Crystal Palace have already turned down an offer of around £35m from Galatasaray for the winger, with Al Hilal also showing interest in his situation, and their stance has been that any sale depends on first identifying a replacement — a condition the club is not close to meeting.
Palace's transfer business elsewhere in attack is also live.
Aston Villa and Juventus are both expected to renew their interest in Mateta before the window closes, with the France striker's future at Selhurst Park similarly uncertain as Palace weigh up whether letting one attacking player leave without cover in place is a risk worth taking this close to deadline day.
For Liverpool, any move for Sarr would sit alongside their pursuit of Barcola under new head coach Andoni Iraola, who has prioritised rebuilding the wide areas of his squad since replacing Arne Slot.