Ferguson underwent emergency brain surgery on Saturday.
In their statement, the club added: "His family request privacy in this matter".
When it emerged Sir Alex was in hospital, football fans - including names from the worlds of sport, politics and television - set allegiances aside to unite in sending their best wishes to one the game's greats.
It comes after son Darren Ferguson skipped his Doncaster side's League One match against Wigan Athletic on Saturday.
"I went to see him in the box after the game on Sunday". "I hope he has a full recovery".
News of Ferguson's operation was made public by United in a statement that appeared to be cautiously optimistic about his prospects for recovery. "Everyone at Manchester United sends our very best wishes".
David Beckham, who came through at United under Ferguson, wrote on Instagram: "Keep fighting Boss".
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The 77-year-old called on ministers to explain how the situation could have been allowed. Gran Trixie Gough, 76, from Norfolk, died in 2015 from breast cancer.
City boss Pep Guardiola had earlier told Sky Sports ahead of the champions' 0-0 draw with Huddersfield: "Brian Kidd, who is here now, was with [Sir Alex] for a lot of time, so a big hug and our thoughts are with his wife Cathy and the Manchester United family".
"My thoughts and prayers are with you, my dear friend".
Managers Sam Allardyce of Everton and Southampton's Mark Hughes, a former United player under the Scot, also added their best wishes following the first Premier League game after the news broke. Thoughts with all the family.
Twitter user @TheRainbowStand said: "Nobody greater at comebacks/recovering".
Another former United goalkeeper Peter Schmeichel tweeted simply: "Please. Be strong. Win this one".
"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 Guardiola after City lifted the trophy following a goalless draw at home to Huddersfield.