Dmitris Dmitriadis, who is also Ukraine's honorary consul in Greece, told BNS the court ruling is expected on February 9. The court has already heard the case but has postponed its ruling several times due to various reasons.
Radkevich was detained in Greece last September, but it took some time for the authorities of the two countries to ascertain his identity.
He was detained in Greece on a European arrest warrant issued by a Lithuanian court in August.
Radkevich, 53, was sentenced to four years in prison for driving a tank involved in the events at the Lithuanian capital's Press House.
His imprisonment in Lithuania could lead to political tensions between Vilnius and Kyiv, because he is a veteran of Ukraine's war against Russia-backed separatists.
The man is one of 67 people handed prison sentences in the mass trial. The majority of the defendants were convicted in absentia as Russia and Belarus refused to extradite them.
Fourteen civilians were killed and hundreds more were injured when the Soviet troops stormed the TV Tower and the Radio and Television Committee building in Vilnius in the early hours of January 13, 1991.
The Soviet Union used military force in its attempt to remove the legitimate government of Lithuania which declared independence on March 11, 1990.