[2][3] Throughout his sporting career, Aslanasvili trained full-time for Atlas Kallitheas Wrestling Club in Athens, under personal coach Michail Charachura.

Aslanasvili qualified for the naturalized Greek squad in the men's lightweight class (60 kg), when Greece welcomed the world to the 2004 Summer Olympics in Athens.

He filled up an entry by the International Federation of Association Wrestling and the Hellenic Olympic Committee, as Greece received an automatic berth for being the host nation.

[2][4] Amassed the home crowd inside Ano Liossia Olympic Hall, Aslanasvili opened the prelim pool with a shut out 5–2 victory over neighboring Albania's Sahit Prizreni, before losing to Iran's Masoud Mostafa-Jokar by a rigid 3–2 decision.

Placing second in the pool and eleventh in the final standings, Aslanasvili's performance was not enough to put him further into the medal rounds.