The 33-year-old centre half was signed on short-term deal from manager Rafa Benitez's old club Valencia in January and played 12 Premier League games for the club.
A substitute appearance for Valencia in the early rounds of the Champions League made Pellegrino ineligible to take part in Liverpool's triumphant European Cup campaign.
Pellegrino was twice on the losing side in a Champions League final with Valencia but came on as late substitute when the club won the UEFA Cup in 2004.
