The 22-year-old Paraguayan was expected to be the latest addition to Brendan Rodgers' squad at Anfield, but the move has collapsed after he failed to secure a work permit to play in England.
The Benfica star has not played enough matches for the Paraguay national team to qualify for a permit - he's only made one appearance for his country.
The report claims Rodgers will now turn his attention elsewhere, but will continue his search for competition for current first-choice full-back Jose Enrique.
Promising youth team player Jack Robinson has joined Blackpool on loan, opening up a space in the Liverpool squad for a player to challenge the Spanish left-back for a starting berth.
Melgarejo was expected to join Iago Aspas and Luis Alberto - the recent Liverpool signings - on Merseyside, but the Reds will now look at two other full-backs instead.
Top of the shortlist is Valencia left-back Aly Cissokho, while another La Liga star - Guilherme Siqueira from Granada - has also been linked with the Anfield club.