The Argentinian full-back was signed in 2007 by Rafael Benitez as a potential star for the future from Boca Juniors, but has failed to live up to expectations on Merseyside.
After an impressive beginning to his time in the senior ranks, Insua appeared to be destined to become a fixture at Anfield as he gained first-team experience.
However, with first choice Fabio Aurelio suffering a series of injuries, the Reds' reliance on the 21-year-old to play regularly at left-back appeared to hamper his form and confidence in a struggling team, which saw him lose his place towards the end of the season.
Fiorentina have been rumoured to be interested in the player for several weeks, but despite Hodgson admitting he was impressed by his talent, he conceded that Insua may move on, with a bid rumoured to be on the table at around £5million.
"I saw him play in the last three days and I like him both as a player and on a personal level," Hodgson told Radio Blu in Florence.
"However, talks with Fiorentina started before I got here, so I don't know how advanced they are.
"I cannot say if Insua will stay at Liverpool or not. I'll have to discuss that with the club."
Fiorentina's director of sport Pantaleo Corvino confirmed talks are ongoing between Liverpool for Insua.
"Insua? It is a negotiation like many other, you have to wait to see how it will finish."