Both the Gunners, who have money to spend according to chief executive Ivan Gazidis, and Turkish giants Fenerbahce are tracking the 22-year-old, according to his representative.
The Paraguayan appeared for Aguais in their Europa League final defeat to Chelsea in May and is said to be valued at 5 million pounds with Turkish side Fenerbahce also interested - though neither team has made an offer for the 22-year-old.
"Arsenal and Fenerbahce have inquired about Melgarejo but so far there has been nothing concrete," revealed Appleyard to Radio Monumental.
Melgarejo, who joined Benfica from Paraguayan side Independiente in 2011, has made just one senior appearance for his country, coming off the bench in a friendly against Guatemala in November.
The youngster featured in 39 games for the defeated Europa League finalists last season, scoring two goals and bagging five assists.
Arsenal chief executive Ivan Gazidis has recently claimed Arsenal fans can expect a busy summer, with at least 70m pounds thought to be at Arsene Wenger's disposal, as it looks to strengthen its squad ahead of next season's title challenge.