The Argentine, who has a solitary international cap, is travelling to Italy to discuss personal terms.
"We have agreed a fee for the sale of Emiliano Insua to Fiorentina and given them permission to speak with the player," a Liverpool spokesman said on their website (www.liverpoolfc.tv).
"Emiliano has now left our Swiss training camp and we'll make further comment when appropriate."
Insua, 21, arrived at Liverpool in 2007 from Argentina's Boca Juniors, played 62 games for the Merseyside club and scored one goal.