Alexander Vinnik, who headed BTC-e, an exchange he operated for the cyber currency, was indicted by a US court in July on 21 charges ranging from identity theft and facilitating drug trafficking to money laundering.
Last week, Thessaloniki judges ruled that he could be handed over to the United States, but they have now also ruled the Russian extradition request admissible.
Greece’s justice minister will make the final call whether he will be handed over to the US or Russia.
Vinnik said Wednesday he wants to be extradited to Russia, where the government has said it should get priority over the US because he is a Russian citizen.
Vinnik has lodged an appeal against last week’s decision favouring the US request, and that case will be heard by the Greek supreme court.
The Russian has been languishing in a Greek jail since his arrest on July 25 in the tourist resort of Halkidiki, near Thessaloniki.
According to US authorities, Vinnik “stole identities, facilitated drug trafficking, and helped to launder criminal proceeds from syndicates around the world”.
Vinnik, whose defence is run by Greek star attorney Alexandros Lykourezos, has denied the charges.
BTC-e, founded in 2011, became one of the world’s largest and most widely used digital currency exchanges, but according to the US indictment, it was “heavily reliant on criminals”.