Simunovic joined Celtic during the summer transfer window, but he has not been selected to make an appearance for Ronny Deila's side so far.
The defender's lack of time training with his new teammates has been cited as the reason for his omission to date, but Kennedy says that he is now up to speed and could be involved on Thursday.
“He’s fit, he’s come in and trained well," Kennedy said. "The weekend was too early for him after having very little time with the group – it would have been a big ask.
“But he’s training well and he’ll certainly travel with the group for Thursday.”
Celtic will be keen to impress in Europe this season, despite dropping out of the Champions League.
The Bhoys did reasonably well in the Europa League last term, before dropping out against Inter Milan in the Round of 32.
Deila's men are under pressure to impress against Ajax, as their start to the season has been poor, and they will need Simunovic to hit the ground running if he does play.
Celtic's defence has looked vulnerable so far this term, with the loss of Jason Denayer and, more recently, Virgil van Dijk clearly affecting the team's performance levels.
Simunovic's task will be to help cover the loss of key personnel, and he will be keen to make a good first impression on Thursday.