Fernando Gago's agent claims Liverpool would be "a perfect club" for the Real Madrid midfielder to continue his career after being told he is surplus to requirements at the Santiago Bernabeu.
Liverpool's director of football Damien Comolli is believed to have already opened talks with Gago's representative, Marcelo Lombilla, regarding a possible move for the defensive midfielder.
Gago, 25, does not feature in Jose Mourinho's plans for the new Primera Liga season and is reportedly keen on a move to Anfield after speaking to former Reds Xabi Alonso and Alvaro Arbeloa about life on Merseyside.
Lombilla said: "Gago needs to play and Liverpool would be a perfect club for him, Fernando wants to get back on the pitch and return to the top level and at the moment that is not possible in Madrid."
Real are believed to be demanding £15 million for the Argentina international but Liverpool are eager to secure a cut-price £10 million deal after splashing out £16 million on Sunderland midfielder Jordan Henderson.
There has also been interested from a number of other clubs and a source at Madrid told the Daily Star: "Fernando knows that he has no future at the club. There has been interest in the past from some Italian clubs and Aston Villa, but Liverpool have shown the most interest."