In a tweet, the club wrote: “Sir Alex no longer needs intensive care and will continue rehabilitation as an inpatient.
“His family have been overwhelmed by the level of support and good wishes but continue to request privacy as this will be vital during this next stage of recovery.”
The update comes after the former football manager, 76, had emergency surgery on Saturday after suffering a brain haemorrhage.
Following the operation, Manchester United said it had gone “very well but he needs a period of intensive care to optimise his recovery”.
Messages of support from the world of football and beyond poured in following news that the Manchester United legend was in intensive care.
Among the heartfelt messages, Real Madrid and ex-United star Cristiano Ronaldo told Sir Alex to “be strong”, while David Beckham urged his former manager to “keep fighting”.
Earlier on Wednesday, Manchester United’s current manager, Jose Mourinho, said the club was “confident” the Scotsman would make a swift recovery.
At a pre-match news conference, Mourinho said Manchester United were “very positive” about Sir Alex’s health following his surgery.
The former manager retired from his role at United in 2013 and became a director after 26 years in charge and remains the most successful manager in British football history.
He won 38 trophies during his time at Old Trafford, including 13 Premier League titles, two Champions League crowns, five FA Cups and four League Cups.