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
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"Arsenal and Fenerbahce have enquired 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 thought to be at Arsene Wenger's disposal, as they look to strengthen their squad ahead of next season's title challenge.