Ferguson, who won 38 trophies during an unrivalled 26-year reign at Old Trafford, needed emergency surgery last weekend after a fall at his home near Manchester.
British football's most successful manager remains in intensive care, but the early signs of his recovery are positive.
One expert, Dr Peter Hamlyn, said the football legend and father-of-three could make a full recovery but his progress will have to be monitored closely.
All of us wish Ferguson the very best in his recovery. So when you find one of them you have to value and you have to keep and in this case is not about me, it is about the club. "He is a strong man and an optimistic man".
The manager does not believe there is a cloud over the club and described the spirits of players and staff as good.More news: The Players Championship: Phil Mickelson praises Tiger Woods' past form as 'unrepeatable'
Mourinho said midfielder Michael Carrick will captain the side when he plays his final match against Watford on Sunday.
"All the Manchester City fans in the stadium, you can not find one person who does not wish the best for an wonderful person", said City boss Guardiola.
Chelsea manager Antonio Conte added: "I have had the chance to know him and his wife". I understand that this is a special person.
The haemorrhage is a bleed between the skull and surface of the brain, which usually starts with a sudden "thunderclap" headache so painful that many people lose consciousness.
Ferguson's family are said to be "pleased and encouraged" by his progress since the operation, though no timescale has been placed on his health and, or when, he will be allowed to leave hospital.
"They all work well, even in weeks [following] bad performances or bad results", he said. When I heard the news my heart dropped straight away; I want to wish him and the family all the best.