Ronaldo, 34, will spearhead the Italian champions' attack against the young Dutch outfit alongside Federico Bernardeschi on Tuesday, with Allegri still to decide on a third striker to replace Croatian Mandzukic.
Portuguese star Ronaldo came back from injury to score a crucial away goal in last week's 1-1 draw in Amsterdam, having bagged an incredible hat-trick to rescue their campaign in the last 16 against Atletico Madrid.
"Thank God he's playing for us and not the opponents," Allegri told a press conference in Turin as he outlined his selection headaches on the eve of the game.
"Cristiano has extraordinary quality. In certain moments he becomes an unstoppable player and you can see it on his face," said Allegri
"From a physical point of view he's better, he's got great skill and quality and during a match becomes a different player."
But the Juventus coach ruled out making the five-time Ballon d'Or winner his team's skipper in the absence of defender Chiellini.
"Ronaldo captain? If (Paulo) Dybala plays it will be Dybala otherwise it will be (Leonardo) Bonucci," said Allegri.
Allegri said he had yet to decide between Argentine forward Dybala and teenager Moise Kean, who has scored six goals in as many games.
"Mandzukic was not called up because he had a knee problem. We need to have players in good shape," said Allegri.
"I still need to decide who starts in attack, it could be Dybala or Kean or neither of them. If one of them plays, then one of Mattia de Sciglio and (Joao) Cancelo will be left out.
"It depends on what I decide to go with tomorrow night."
'Young team playing like adults'
Winger Douglas Costa is "not in the best physical shape" after a calf problem and won't be able to play the whole game, but could play for half an hour.
Midfielder Emre Can returns from injury after missing the first leg, and sat alongside Allegri in the press conference.
"I watched the game on TV, it's impressive how they play, but we're not afraid of them and we want to play our game and win tomorrow." said the German. "We have to go with the same attitude as game against Atletico. For sure we won't play for 0-0."
Allegri added: "In Amsterdam we could have, and should have done better. I expected goals to be scored I have the same expectations for tomorrow."
Ajax coach Erik Ten Hag conceded that Juventus were the favourites, as key midfielder Frenkie de Jong, 21, still remains a doubt for the Dutch league leaders with a hamstring problem.
"After tonight's training, we will see," said Ten Hag.
"This is the perfect challenge for us. After 1-1 in Amsterdam they are favourites.
"Being able to beat Real Madrid was a remarkable achievement and hopefully tomorrow we'll be able to have another memorable match," he warned.
"We believe we can definitely compete with these giants.
"We're a young team but play like adults, we showed it against Real Madrid."