Many of Sir Alex's former players and other stars have posted get-well messages for the 76-year-old, who spent nearly 27 years in charge before retiring in 2013 as the most successful manager in British football history.
Ferguson underwent emergency brain surgery on Saturday.
"Sir Alex Ferguson has undergone emergency surgery today for a brain haemorrhage", the statement said. Ferguson's family have requested privacy as he recovers in Salford Royal Hospital. Phenomenal. He's in our prayers and thoughts, we hope him a speedy recovery and send all our love to him.
An ambulance was reportedly called to his Cheshire mansion at 9am (on Saturday) before taking him to Macclesfield district hospital.
"The greatest manager I've ever seen. As a personal friend, I hope he has a full recovery".
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BC-SOC-Man United-Ferguson, 2nd Ld-Writethru, 178'Win this one': Man U's plea after Ferguson's brain surgeryAP Photo LON880, LON179Eds: Adds detail.
David Beckham, who came through at United under Ferguson, wrote on Instagram: "Keep fighting Boss".
Current World Player of the Year Cristiano Ronaldo, who previously played for United and is now signed to Real Madrid, tweeted: "My thoughts and prayers are with you, my dear friend. Be strong, Boss!" he said. "Thoughts are with the family and close ones".
Edwin van der Sar: Devastated about the news about Sir Alex and knowing all too well about the situation ourselves.
Twitter user @TheRainbowStand said: "Nobody greater at comebacks/recovering".
"No updates, just an endless list of tweets from the 4 corners of the world showing support and love. Be strong. Win this one" interspersed with prayer emojis.
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Born into a family of shipyard workers in the Govan area of Glasgow, Sir Alex has been a well-known Labour supporter and has been named in the past as one of the party's biggest donors. Thoughts are with him and his family.
"Firstly, because at Arsenal we care, we would like to wish Alex Ferguson to get well very quickly", he said at the start of his speech.
Ferguson has been coaching Manchester United for 27 years (1986-2013) and won 38 trophies, including 13 championships in England and two Champions League. His son and wife, Cathy, were with him, the Guardian reported.
"He needs a period of intensive care to optimise his recovery".
Italian Serie A sides AC Milan and Inter Milan, Spanish LaLiga champions Barcelona and Scottish title winners Celtic were among a host of other football clubs, along with the National Basketball Association, to send get-well-soon tweets.
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