Andreas Dossena and Fabio Aurelio both left the club last season, leaving Liverpool without an established left back.
A LFC 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.”
When the sale goes through, Liverpool will have netted roughly £14M in player sales since January alone.