The Inter boss has several times been linked with the United job, should Fergie decide to retire.
Robson told the Sunday Mirror: “I just don’t agree when I hear people say that Jose is the perfect boss to take over from Sir Alex.
“Jose is a great coach and the things he achieved at Porto and Chelsea mean he commands huge respect.
“But Manchester United aren’t just a club who only want to win things. The fans demand that success is achieved by playing the Manchester United way.
“Attacking football is a vital part of the club’s heritage. For me, Jose Mourinho is too cautious in his approach to the game to be manager of Manchester United.
“The important thing for any manager who follows in Sir Alex Ferguson’s footsteps is to recognise the traditions of Manchester United and maintain them.”
He added: “United’s owners won’t be looking forward to the day when they have to find a successor to Sir Alex – but I think that’s still a long way off.
“It doesn’t matter how many trophies United win this season, Sir Alex won’t be thinking about retiring.
“United could win all five, but I still can’t see him walking away from the club. From what Sir Alex has told me, the only thing he considers when it comes to retiring is his health and fitness.
“I think he reckons he has at least another couple of seasons after this one left in him. It won’t matter whether United wine very thing or nothing this season, he’s planning to be here next year.
“He has got an amazing desire to win things – that is the secret to his longevity.
“He loves Manchester United, has a great passion for football and has this inner desire that drives him to want to win all the time.”