Brendan Rodgers also has the option to buy the Paraguayan for around £7 million next summer, if the temporary move proves successful
Brendan Rodgers also has the option to make the move permanent for a fee of approximately £7 million at the end of the campaign.
The 22-year-old, who can also play at full-back is being brought to Anfield to provide competition for Jose Enrique, with Rodgers keen to strengthen his defensive options before competing for a top-four place this term.
Melgarejo made 35 appearances in all competitions for Benfica last season, including the club's Europa League final defeat to Chelsea in May.
Liverpool's move for the Paraguay international hinges on whether a work permit can be obtained as Melgarejo has secured just one senior international cap.
Melgarejo has also been linked with a move to Arsenal and Turkish side Fenerbahce this summer.