United confirmed on Thursday evening that Ferguson was now out of intensive care, as they suggested their record breaking former manager needs time to recover.
The 76-year-old former United manager is to continue his rehabilitation at Salford Royal in hospital.
"Sir Alex no longer needs intensive care and will continue rehabilitation as an inpatient", United said in a statement on Twitter.
The family continue to request "vital" privacy as Ferguson enters the next stage of his recovery.
Mourinho is the third manager since Ferguson's retirement in 2013 to be unable to win the Premier League trophy that the Scot collected 13 times.
Ferguson is now out of intensive care after being admitted into hospital on Saturday following a fall at his Cheshire home.
The pair had been together in public less than a week before news emerged of Ferguson's condition, as they presented outgoing Arsenal manager Arsene Wenger with a gift during the Premier League match at Old Trafford on April 29. "I went to see him in the box after the game and he looked in a ideal shape", said Wenger, after his final home game as Arsenal boss at the Emirates.
Speaking on Wednesday at a press conference, Mourinho said: "His family asked for privacy and that's what I am going to respect".
Sunday saw runaway winners Manchester City, United's local rivals, receive the Premier League trophy as Guardiola added an English title to the Spanish and German ones he won in charge of Barcelona and Bayern Munich respectively.
Ferguson, the most successful manager in Manchester United's history, had surgery on Saturday.
And Liverpool manager Klopp described Ferguson as "absolutely the boss".
"All the Manchester City fans in the stadium, you can not find one person who does not wish the best for an wonderful person", City manager Pep Guardiola.
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