Emiliano Insua is to hold talks with Fiorentina after Liverpool agreed a fee to sell the defender to the Italian club.
Fiorentina have been heavily linked with a move for the left-back in recent weeks and an offer, reported to be in the region of £5million, has now been accepted.
Liverpool have confirmed that the Argentine has left the club's pre-season training camp to discuss a switch to Serie A.
A club spokesman said: "We have agreed a fee for the sale of Emiliano Insua to Fiorentina and given them permission to speak with the player.
"Emiliano has now left our Swiss training camp and we'll make further comment when appropriate."
Insua made 31 appearances in the Premier League for the Reds last season and has featured a total of 62 times since his arrival from Boca Juniors in 2007.
New Liverpool boss Roy Hodgson is now likely to be in the market for a left-back after Fabio Aurelio left Anfield at the end of last season.
Meanwhile, Liverpool's opening pre-season friendly against Al-Hilal in Austria has been called off due to a waterlogged pitch.
Several pitch inspections were conducted before the match was postponed, meaning Hodgson will have to wait until Wednesday's fixture with Grasshoppers for his first match as Liverpool manager.