Biglia, 29, has attracted interest from all over Europe since his impressive displays for Argentina at the 2014 World Cup.
His arrival into the international side from the quarter-finals onwards saw the midfielder form a strong partnership with Barcelona star, Javier Mascherano.
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And he could be just what Klopp needs on Merseyside given his credentials. A midfield enforcer, Biglia's consistency and lack of injuries woud prove hugely beneficial to a Liverpool side currently suffering from an ever-growing injury list.
However, being on the wrong side of his 20's, the Reds must seek to act now rather than later if they're to get the best out of the Serie A star.
The attraction of Biglia can't be understated either. Numerous reports suggest the likes of Real Madrid and Inter Milan, Lazio's Serie A rivals, are very much in the hunt for the captain's signature.
And given that the Argentine has only recently been handed the captain's armband, it will likely take a huge offer from Liverpool to tempt him from Rome to Merseyside, though Biglia has reportedly stated a regular starting place could be enough to lure him away from Italy.
However, €30 million is the asking price, with Lazio president Claudio Lotito seemingly stubborn to go anywhere below it.
The quality is there, but is the worth? Such a huge fee for a player entering the latter stages of his career is a potentially risky investment for Liverpool owner John W Henry.
If this transfer does get the go ahead, though, Klopp will be hoping for more of the same from Biglia as he looks to drag Liverpool back into the top four.