Vardy and Maguire were both in action for England at the 2018 World Cup, and the pair are yet to return to training.
Leicester will open their 2018-19 Premier League season against United at Old Trafford on August 10, and Puel has conceded that the duo are unlikely to be involved due to their lack of training.
"If we are serious I think they cannot participate in the first game, with just five days training with the team. They normally need more time, but we will see together with calm," Puel told reporters.
"We don't rush these players. It is important after the World Cup to work but also come back with the team and live with the team to find again the atmosphere of the club and the squad.
"Of course Jamie and Harry are valuable players for us but we need to protect them. If they are available to play in their minds it is a good thing... but we have to take a protective decision from us."
Leicester will round off their preparations for the new campaign with a friendly against Lille this weekend.