The centre-back has missed the last three matches the Bhoys have played, but it seems that his return to the first-team fold could be imminent.
That is good news for the Bhoys as his replacement, Efe Ambrose, picked up a red- ard in their most recent match against Hearts and is set to miss their next domestic game through suspension.
JK on Simunovic: Started light training again. Efe has come in and done really well in his absence.— Celtic Football Club (@celticfc) September 28, 2015
Simunovic made a positive impact on his debut for Celtic against Ajax in the Europa League, but he has been unable to build on that performance.
The 21-year-old added composure and solidarity to Celtic's backline, as they picked up a point at the Amsterdam ArenA, and manager Ronny Deila will be keen to have him back.
Simunovic was one of the club's most exciting summer recruits and he will be hoping to make up for lost time, when he does hit fitness again.
Celtic will need the Croatian to hit the ground running too, as they are currently trailing Aberdeen in the Scottish Premiership title race.