Chile international Vidal missed Juve's 2-0 Serie A victory over Udinese on Saturday with a persistent knee problem, while midfield partner Pirlo sustained a hamstring injury at the end of August.
Coach Allegri revealed that Vidal could return in time for the Serie A champions' clash with Milan on Saturday and Pirlo's fitness is set to be assessed at the end of this week.
"We hope to have Arturo Vidal back with us for Milan on Saturday," Allegri said at his pre-match news conference. "Pirlo's coming on well. He'll up his workload and we'll give him another look over at the end of the week."
Juve start their UEFA Champions League Group A campaign at home to the Swedish champions on Tuesday and Allegri will be determined to succeed where Antonio Conte failed last season, by guiding his side into the knockout stages.
The Turin giants should possess too much quality for Malmo, but Allegri stressed the importance of not taking the underdogs lightly.
"Juve need to try and remain at the level of the top European clubs, but for now the minimum aim is getting out of the group," he added.
"The most immediate target is winning tomorrow's game. There are no easy encounters in Europe.
"The group may seem easy but nothing is ever straightforward in the Champions League. Malmo are a very quick and physical side."
Centre-back Giorgio Chiellini is also set to feature after missing the start of the domestic season through a combination of suspension and a calf complaint.
And the Italy international is itching to get involved, saying: "I'm in good shape and available for tomorrow's game.
"There's plenty of enthusiasm in the camp and around Turin. We want to do well in the Champions League."
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