Reds boss Rafael Benitez is keen to add the £17 million-rated midfielder on a permanent deal after signing the midfielder on loan from West Ham last year.
But the club's reluctance to come up with the funds required have opened the door for others to open negotiations with the Argentina international, and Serie A giants Juventus are reported to be lining up a summer move.
"I would love to stay here (in Liverpool). I have tried and I've adapted to the city very well.
"But the clubs that are talking are also important and I would like to go," the 23-year-old told an Argentinian radio station.
The player's agent Walter Tamer said "Liverpool have not made any offer at all to buy Javier and it is likely that he will go to Italy next season."