After widespread speculation, Van Gaal's sacking was confirmed on Monday, just two days after he led the club to FA Cup success by defeating Crystal Palace at Wembley.
Mourinho, a three-time Premier League winner with Chelsea, is expected to be announced as Van Gaal's successor this week, as United look to regain the glory years of the Alex Ferguson era.
Van Gaal's style of play drew criticism from large numbers of United fans but Cantona, who helped the club to four league crowns in the mid-1990s, believes Mourinho's philosophy may not endear him to the Old Trafford faithful, either.
"I love Jose Mourinho, but in terms of the type of football he plays I don't think he is Manchester United," Cantona told the Guardian.
"I love his personality, I love the passion he has for the game, his humour. He is very intelligent, he demands 100 per cent of his players. And of course he wins things.
"But I don't think it's the type of football that the fans of Manchester United will love, even if they win.
"He can win with Manchester United. But do they expect that type of football, even if they win? I don't think so."
Asked what he thought had gone wrong at United over the past three years, Cantona replied: "They miss me.
"I think they have lost something. You can feel it. But it's difficult to come after someone who has been at the club 25 years.
"Even if you are a great manager, the fans still feel the philosophy of Ferguson."
