The Sporting Lisbon man has emerged as the first choice left back for Argentina ahead of the summer’s World Cup, while he is also capable of playing at centre back.
Brendan Rodgers had scouts present for Sporting’s 1-0 win over Porto at the weekend, with reports in Portugal suggesting they were casting their eye over 23-year-old Rojo.
Rodgers is keen to strengthen at left back next season, with Aly Cissokho set to return to Valencia after a season long loan, and Jose Enrique continuing to struggle for fitness.
Spaniard Enrique has not featured since October, and was recently sent to America for tests on a serious knee injury.
Rojo has made the left back position at Sporting his own since signing from Spartak Moscow in 2012.
However, a move may be complicated by the fact that 75% of Rojo ‘s contract is owned by a third party – investment company Doyen sports.
Premier League rules mean that the Reds would have to buy the defender outright from both Sporting and Doyen Sports.