Ferguson has celebrated his 70th birthday and the 25th anniversary of his appointment at Old Trafford this season and is showing little sign of slowing down. Because of that, Robson, Ferguson's former captain, does not think the club have even thought about the identity of their next manager.
But Robson knows the time will come when the issue has to be dealt with and he feels Real Madrid's former Chelsea boss would be a good fit. The former England captain said: "How do you replace Sir Alex Ferguson? It is near enough impossible. Mourinho is definitely one who would be up at the top of the list. His record speaks for itself."
Aside from the suitability of Mourinho, who has won the Champions League with Porto and Inter Milan, Robson feels United might have other candidates closer to home.
Robson has been impressed with the work of Ferguson's assistants Mike Phelan and Rene Meulensteen and would consider them as good options.
Robson said: "Whoever goes in there they will have their opinions and ideas, but because of the success United have had over the last 20 years, you can't go in and rip everything apart and try to rebuild the way you think it should be.
"How can you do that after so much success?
"Why not Mike Phelan and Rene take over from Sir Alex Ferguson when he does decide to pack in.
"That never gets mentioned but they know how it works. It has always has to be someone who is really well known with a track record."