Charlie, 10, remains in a serious but stable condition at Alder Hey Children's Hospital after emergency surgery following a head-on car crash near Macclesfield.
Sir Alex was preparing Manchester United for Tuesday's Champions League semi-final against Arsenal when he heard about the accident.
Charlie's six-year-old sister Grace - the United manager's grandaughter - and their mother Nadine were also badly hurt.
Sir Alex's son Darren, who is Nadine's ex-husband and Grace's father, also visited the hospital. The exact nature of the injuries to Charlie, who is Nadine's son from a previous relationship, have not been revealed.
The accident happened on Lower Trap Street, Lower Withington, as the children were being driven to school.
Witnesses say the stretch of road is a blackspot. Lynda Syers, 60, told how she heard `the most horrendous bang' yards from her home before four ambulances and an air ambulance arrived.
She said: "I could see the mother and her children trapped in the car and the boy had a really nasty gash on his head."
Nadine, 30, was airlifted to Wythenshawe Hospital and had emergency surgery after suffering injuries to her leg and ribs. She is in a stable condition. Grace suffered less serious chest and head injuries, and is stable at Crewe's Leighton hospital.
Nadine was driving a Vauxhall Corsa when it was in an accident with a Fiesta travelling in the opposite direction. The driver of the other vehicle, who is 17, was taken to Macclesfield hospital with leg injuries.
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Mykiel, Madison Connecticut CT 06443 USA (07/05/2009 at 09:08)