Moyes, the 50-year-old Everton manager, has long been admired by those in senior positions at Old Trafford for the excellent job he has done, on limited resources, at Goodison Park in the past decade.
Mourinho, too, is highly regarded, though that was not always the case. He was seen as too arrogant and cocksure by the decision makers at Old Trafford, though not by Ferguson who recognises his talent and views his arrogance as self-assuredness.
Ferguson will have a say in United's next appointment, along with the outgoing chief executive David Gill, his replacement Ed Woodward, the club legend and director Sir Bobby Charlton, plus the Glazer family, who own the club.
Mourinho went on a charm offensive after his Real Madrid side had knocked United out of the Uefa Champions League in March, in part because he knew his time at the Bernabeu was coming to an end and because he was soliciting potential future employers.
No other names are being linked with the about-to-be-vacant Old Trafford position and Ferguson, who will become a United director, did not mention a successor in his parting message, delivered on the club website shortly after 9am UK time (noon UAE).
“The decision to retire is one that I have thought a great deal about and one that I have not taken lightly,” Ferguson said. “It is the right time.
“It was important to me to leave an organisation in the strongest possible shape and I believe I have done so. The quality of this league-winning squad, and the balance of ages within it, bodes well for continued success at the highest level while the structure of the youth set-up will ensure that the long-term future of the club remains a bright one.
“Our training facilities are among the finest in global sport and our home Old Trafford is rightfully regarded as one of the leading venues in the world.
“Going forward, I am delighted to take on the roles of both director and ambassador for the club. With these activities, along with my many other interests, I am looking forward to the future.
“I must pay tribute to my family, their love and support has been essential. My wife, Cathy, has been the key figure throughout my career.”