1255 GMT February 19, 2020
Widely considered to be the most successful manager in the history of British football, Ferguson, 76, won 38 trophies in more than 26 years in charge of United, including 13 Premier League titles and the Champions League twice, AFP reported.
Britain's Mail Online said the Scot, who retired in 2013, was out of a coma and showing promising early signs of recovery following the hemorrhage on Saturday.
"Surgery went very well and the 76-year-old's response to treatment has given encouragement and cautious optimism to those close to him," the report said.
"However, they recognize it will still be a slow road to full recovery as he continues to be assessed."
"The prognosis is good and his closest friends in football are being kept abreast of any developments," a source told The Sun newspaper.
United midfielder Michael Carrick, who played under Ferguson, has spoken of the respect in which his former boss is held.
"The whole football world is incredible but outside of that as well, from all corners of the globe and different walks of life, people have shown their support," he told MUTV.
"That's the effect he had on people. It was the effect he had on everyone. He means a lot to me, as he does to this club."
"We were all praying for him and thinking of him, Cathy and the family," said Carrick. "It's a tough time for everyone but I'm thinking positive and hoping he will pull through."
United has thanked the many well-wishers, including Premier League managers Arsene Wenger, Pep Guardiola and Jurgen Klopp, who have spoken of their admiration for Ferguson.
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.
However, they later became friends and with Wenger leaving Arsenal at the end of the season, Ferguson presented his old adversary with a memento on his final visit to United's Old Trafford ground just last weekend.
"I was with him on the pitch last week. I went to see him in the box after the game and he looked in perfect shape," said Wenger, after his final home game as Arsenal boss on Sunday.
"He told me he is doing a lot of exercise, and he looked very happy but that kind of accident can happen. We wish him all well and to recover very quickly. He is a strong man and an optimistic man."