The French striker meanwhile is open to leaving the London club as part of any deal that could materialise, according to his agent.
Higuain's buyout clause stands at €94m and Arsenal are hoping that offering Giroud as part of the exchange may convince the Italians to sell.
"If he was asked to leave, then we would evaluate his options," Giroud's agent Michael Manuello stated.
"There is no fear from Olivier about possibly going to Napoli: it is a magnificent city. In Campania, my client could lead a wonderful life.
"Not to mention that the type of game played by [coach Maurizio] Sarri could enhance the quality of a centre forward like him.
"Olivier is an Arsenal player. So far there has not been any communication [with Arsenal] or contact with Napoli. If Arsenal tell us to leave, then things change."
Were the Gunners able to make the deal happen they would be adding the Serie A's golden boot winner to their arsenal.
Higuain scored 36 goals last season as Napoli finished runners-up to Juventus.