The Irishman spent seven seasons at Parkhead before moving to Russia, but insists his loyalties will only lie with his current club.
"It'll be the first time I've faced Celtic," the winger told reporters. "I try to catch most Celtic games on TV and I keep up to date with what's going on online. But, obviously, I'm now a Spartak player.
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|13/1||Aidan McGeady is 13/1 with Bet365 to score the first goal in a Spartak Moscow win over Celtic on Tuesday
"To just be back playing at Parkhead, for a different team, it's going to be a great experience.
"When the draw came out my phone was ringing off the hook with everyone phoning and texting me about the draw and how good it was."
Celtic manager Neil Lennon believes McGeady has progressed well since leaving the SPL champions, and considers him to be Spartak's most potent threat.
"He has improved since his days at Celtic," Lennon said. "In the games I have watched Spartak play, Aiden has probably been their best attacking player.
"He looks in good condition. We all know how good he is on the ball but his movement off the ball is excellent. He covers the ground very quickly and he will be a threat.
"He will want to win the game and he will want to play well."