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 Paraguay international is being brought to Anfield to provide competition for Jose Enrique at left-back, 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 defender hinges on whether a work permit can be obtained as Melgarejo has secured just one senior international cap.
The Paraguayan has also been linked with a move to Arsenal and Turkish side Fenerbahce this summer.