United have offered no update on Ferguson's condition since, saying a procedure on the haemorrhage on Saturday had gone "very well" but that a period of intensive care is needed to optimise his recovery.
'Sir Alex no longer needs intensive care, ' the statement read.
"His family have been overwhelmed by the level of support and good wishes but continue to request privacy as this will be vital for recovery".
The 36-year-old midfielder has won five Premier League titles, the Champions League, Europa League, FA Cup, three League Cup trophies and the Club World Cup since joining United from Tottenham Hotspur in 2006.
Former Manchester United winger Andrei Kanchelskis also took to social media to express his joy as the news.More news: Liverpool boss Klopp not happy with Salah dive
Lukaku, United's top scorer with 27 goals this season, suffered a foot injury in a league win over Arsenal last month.
Sir Alex Ferguson and Jose Mourinho greet Arsene Wenger of Arsenal pitchside prior to the Premier League at Old Trafford on 29 April 2018.
Asked if the situation had left a cloud over the club, he added: 'We are positive - very, very positive.
The encouraging prognosis follows an outpouring of concern from across the game over the health of the most successful manager in British football history. During nearly 27 years as manager of United, Ferguson won 38 titles at United.
But the respect held for Ferguson was even clear in City's celebrations as fans held up a banner reading: "Football aside get well Fergie".
Operations to relieve the pressure of excess blood in the brain, as has been the case with Ferguson, are crucial if sufferers are to avoid brain damage or even death. "Everyone thinks it was all this "hairdryer", but the boss enjoys a good time, really enjoys his racing and is good company when you're around him".