Eustathios [Argyros] (Greek: Εὐστάθιος [Ἀργυρός]) was a Byzantine admiral under Emperor Leo VI the Wise (r. 886–912).
Eustathios Argyros first appears during the outbreak of the war with Bulgaria in 894, under the overall command of Nikephoros Phokas the Elder. At the time, he was already patrikios and commander of the imperial fleet (droungarios tou ploimou), and he was sent to the Danube to ferry across the allied Magyars and put pressure on Bulgaria from the rear; the strategy worked, and Tsar Simeon asked for peace. As soon as the Byzantines withdrew for negotiations to take place, however, Simeon drove back the Magyars and renewed war with Byzantium.
In 902, Emperor Leo VI the Wise had sent a fleet under Eustathios to aid Taormina in Sicily, which was being besieged by the Arabs. The city fell on 1 August 902, and on his return to Constantinople, Eustathios and the city's garrison commander, Constantine Karamallos, were accused by commander Michael Charaktos of extreme negligence and even treason. Both faced execution, but were saved by the intervention of Patriarch Nicholas Mystikos. Eustathios was confined to the Monastery of Stoudios. The nature of Eustathios' "treason" is unclear from the sources, and the whole episode is complicated by the fact that no source explicitly mentions his presence in Sicily or southern Italy. Modern scholars assume that the fleet's departure was fatally delayed, perhaps, as Theophanes Continuatus claims, because the emperor himself employed its sailors in church construction.