Allegri also said winger Douglas Costa could feature as last season's runners-up try to reach the last eight despite being underdogs having drawn the first leg 2-2 in Turin last month.
Dybala scored the winner against Lazio at the weekend in his first game back from a hamstring injury that ruled him out of the first clash with Tottenham.
Higuain, who scored twice but missed a penalty in the first leg, has been sidelined with an ankle injury for three weeks.
"Both Higuain and Dybala will play. Higuain has been taking part in training for two days, so he is at our disposal and ready to play," Allegri told a news conference on Tuesday at Wembley where his team trained ahead of the clash.
"Dybala is fully fit, as seen against Lazio, but tomorrow is such an important game that they all want to be a part of it, even if not at 100 percent.
"There is a good chance that Douglas Costa will play. They could all play together, they might not. I've only got those three, so some of them have to play."
Mario Mandzukic will miss out because of injury while Federico Bernardeschi, Juan Cuadrado and Benedikt Howedes have also not made the trip.
While Tottenham dominated the first leg after slipping 2-0 behind after 10 minutes, veteran keeper Gianluigi Buffon believes Juventus are at their most dangerous when in trouble.
"It's going to be uphill against a very strong Spurs side but then you can get caught out if it's downhill, so we will be up for the challenge," he said.
"It's obvious there was a certain amount of pessimism after the first leg. One false step and people fear the worst but they don't really take into account the quality of the other team.
"We think we are capable of playing our right game tomorrow. When we have our back to the wall and are wounded, that spurs us on to do even better."
Allegri also said the result from the first leg was not necessarily a bad thing.
"I don't know how Tottenham will play, but considering the first leg result, there's more pressure on them because they are the favourites," he said.
"It's like a final for us and looking back at the first leg, we made a lot of mistakes to gift them chances, so we have to play better technically and take the ball off them, stop them passing it around."
(Reporting by Martyn Herman; Editing by Toby Davis)
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