Signed from Celta Vigo for £7.7 million last summer, the 26-year-old has failed to replicate his La Liga form for the Merseysiders, with just a single goal to his name from 15 stop-start appearances this term.
And it would appear that Liverpool are now willing to cut their losses on the Celta star, in a move that would see them bring Cardozo to the club as potential cover for the current forward pairing of Luis Suarez and Daniel Sturridge.
The Paraguayan boasts an impressive record at Benfica, scoring 113 goals in 174 appearances for O Glorioso during a seven-year spell with the club in which he has won two Primeira Liga titles as well as a Taca de Portugal and a further four Taca da Liga honours.
Cardozo was part of the Benfica team that also made history this season, after completing an impressive domestic treble of trophies.
He was, nevertheless, the subject of some criticism in the wake of their defeat to Sevilla on penalties in the Europa League final, with the 31-year-old one of the players to miss his kick following a deliberately stuttering run up.
The Paraguayan nevertheless accumulated 11 league goals this term and would be a welcome addition at Anfield, given his impressive haul of 33 goals in 71 continental appearances for the Lisbon giants in the Europa League and Champions League.
Aspas may also welcome a move abroad and the chance to rediscover his form with regular playing time.
Benfica are certainly on the lookout for a new striker too, with star youngster Rodrigo rumoured to be close to sealing a move to La Liga with Valencia.