The 22-year-old Paraguayan is valued at £5million and could be one of Arsene Wenger's signings in what will be a crucial summer.
Chief executive Ivan Gazidis has said Arsenal have money to spend and they have been linked with Everton's Marouane Fellaini.
Full-back Melgarejo, who featured in the Europa League final against Chelsea and is also interesting Fenerbahce, is another possible target but Arsenal have not yet made any offer.
"Arsenal and Fenerbahce have enquired about Melgarejo. But so far there has been nothing concrete," agent Juan Gabriel Appleyard told Radio Monumental.