The Reds have ended weeks of speculation over the France international moving to Merseyside by agreeing a deal with European champions PSG for a reported £106M.
Barcola joins Victor Munoz as a new face in Andoni Iraola's attack and Cody Gakpo could now join Manchester City.
England international Elliott spent last season on loan at Aston Villa, but Unai Emery opted against a permanent deal, with the former Fulham star effectively frozen out to avoid triggering a £35M purchase clause in the second half of the campaign.
Iraola has opted against using him in Liverpool's first two games of 2026/27, and an exit looks certain, as he moves into the final year of his contract at Anfield.
BBC Sport are reporting a last minute loan offer has arrived from LaLiga side Valencia with the Spanish giants open to covering half of his wages as part of the deal.
His expiring contract means a loan would effectively be the end of his Liverpool career after winning the 2024/25 Premier League title and making 149 appearances for the club.