Ivanovic had been expected to miss the encounter in Glasgow with an eye injury, but Mancini has hinted that he may include the defender on the substitutes' bench.
The Italian is quoted by BBC Sport as saying: "He is getting better, although he is not 100% yet.
"With his experience he is important to us. Maybe he can play or go on the bench. We will decide on Thursday."
Should Ivanovic play against Celtic, the Serbian international will be making his first appearance in the United Kingdom since leaving Chelsea 12 months ago.
Ivanovic made 377 appearances in all competitions during his time at Stamford Bridge.