He described Sir Alex, who's 76, as one of the greatest ever managers and says he's been told the emergency brain surgery he had on Saturday had gone well.
During his 26 years at Old Trafford, Ferguson - who also led Aberdeen to a European Cup Winners' Cup triumph - took the club to the pinnacle of the English and European game.
Medical professionals have said that the coming weeks will be vital for the former Manchester United Manager's recovery.
Last night the hospital stated that the Scot was "doing well" and friends have said he is "sitting up talking and asking about his results".
Beckham broke into the team in the 1990s as Ferguson turned United into the country's most successful club. Wenger enjoyed a long, and at times fractious rivalry with Ferguson as they battled for Premier League supremacy in the first decade of the Frenchman's long reign in charge of Arsenal. Under his leadership, the team was 13 times champion of England and twice became the victor of the Champions League.More news: Cristiano Ronaldo limps out of El Clasico as Zinedine Zidane provides update
Ferguson's family and Manchester United are yet to release official information on his health.
He tweeted: "My thoughts and prayers are with you, my dear friend".
Rivals Manchester City and Liverpool are among the clubs have sent messages of support to Ferguson, which Carrick said demonstrates Ferguson's importance to the sport.
"This is often life-saving surgery and aims to reduce any long-term disability Sir Alex might suffer with this form of stroke". He then underwent emergency surgery on Saturday.
"It is tragic", Everton manager Sam Allardyce said. But I gather that the operation has been a success.More news: Air France stock shares fall amid strike, CEO's resignation
"Now is the time to pray and hope he can make a full recovery", said Giggs.
If this is indeed the case, the timing of the sign's removal for maintenance is questionable considering the seriousness of Ferguson's condition.
"Every brain injury is unique, as is every individual's recovery".
Ferguson's wife Cathy, and children including son Darren, who is the manager of Doncaster Rovers, were reportedly at his bedside when he awoke from the coma.
He continued: "Sir Alex is a fantastic person on and off the field. When something like that does happen it's nice that the football world comes together and shows support and we are all rooting for him".More news: Azkals drawn fairly in their Asian Cup debut
"I'm hoping he pulls through for a full recovery and my best wishes go out to all his family".