Moyes was odds-on favourite with all major British bookmakers hours after Ferguson's departure.
Other candidates for one of the most high-profile jobs in world football include Real Madrid manager Jose Mourinho, who established a friendly rivalry with Ferguson when in charge of Chelsea and who has made no secret of his desire to return to England.
United's chief executive David Gill outlined the qualities required for the manager's job at Old Trafford and said only a handful of candidates had them.
Gill said the board would seek the opinion of Ferguson and United director Bobby Charlton before naming a new manager.
But former United and England midfielder Paul Ince said there was a risk Ferguson's continuing presence at the club could have a negative effect.
"Whoever comes in to replace him is going to have to deal with the Man United legacy," Ince said. "Replacing Alex Ferguson is such a massive, massive job. Whoever goes in will need the help of Alex Ferguson."