The winger was recalled from his loan spell in Turkey last month and will link up with the squad next week.
The Brighton midfielder sought a January move to Arsenal but remained with the Seagulls.
Giakoumakis remained at Celtic at the end of the transfer window but different deadlines in Japan and the United States mean he can still wrap up a move to suitors such as Urawa Red Diamonds and Atlanta United. "It will get concluded fairly soon," Postecoglou said at a media conference. The 28-year-old went on to make 57 appearances for Celtic across all competitions.