The former VVV-Venlo striker has yet to make his debut for the club since his £2.5m move and won’t start against the Championship side in the Premier Sports Cup quarter final.
However there is a greater likeliehood he will feature than club captain Callum McGrgeor or James Forrest, Postecoglou has revealed. McGregor was forced off during the cinch Premiership win over Ross County earlier this month and missed the trips to Livingston and Real Betis in the past seven days.
Postecoglou said: "Callum won't be back. He's not quite ready. Most of the squad will be the same make-up as the weekend. Giakoumakis is available - probably not to start but he'll be part of the squad."
Neither Forrest nor Christopher Jullien is expected back until after the October international break too.
Defender Jullien has been out since December after suffering knee ligament damage, while winger Forrest has not featured since the 2-0 Europa League win at home to AZ Alkmaar five weeks ago.
Postecoglou said: "I think after the international window I'd expect both of them to hopefully be training with the first team. After that, it will depend on their levels of fitness and how quickly they adapt to what we want to do with our football."
After hosting John McGlynn’s Kirkcaldy side, who have allowed James Keatings to move on loan to Montrose, Celtic play Dundee United at Parkhead on Sunday.