The other leading contender, Jose Mourinho, is not a candidate for the position, senior sources have confirmed.
Ferguson announced on Wednesday that he is retiring as manager after nearly 27 years in charge at Old Trafford.
Sources have told Press Association Sport that Ferguson's successor will be cut from the same cloth as him - with a similar passion for playing attractive football, bringing in top-class players and a strong record in youth development.
United will be looking to the long term with the appointment, rather than a quick fix.
Moyes, 50, may not have won any trophies in his 11 years at Everton but fellow Scot Ferguson himself is a fan of his achievements - and Moyes is out of contract at the end of the season.
Former Manchester United striker Michael Owen said he would choose the Everton boss.
Owen, the former Liverpool striker who played under Ferguson for two seasons, said on Twitter: "What an act to follow. I guess only Mourinho would have the confidence to strut through the door. If it were me, I'd go for Moyes."
Mourinho has made it clear he will leave Real Madrid at the end of the season and he expected to be appointed by his former club Chelsea.
Former United keeper Peter Schmeichel also believes that Moyes would be the best candidate to succeed Ferguson.
He told Sky Sports News: "What we are looking for is, not someone to come in 10 months or three years, we want someone to come stay there and give stability.
"When we talk about Moyes, he has been a decade at Everton and done a fantastic job on limited funds.
"Is he cut from the same cloth? I dont know. Don't forget there will be major changes with David Gill stepping down - the club is really changing in the summer, the more stability they can add the better.
"David Moyes, he sounds like a good solution."
Gill outlined the qualities needed to succeed Ferguson as manager.
"The qualities are the ones that have been inherent at Manchester United for many years," Gill told MUTV.
"Our two most successful eras were with managers who got involved with all aspects of the club, from the youth team to the first team, to get that degree of loyalty and understanding of the football club.
"Clearly he has to have the requisite football experience, both in terms of domestic and European experience.
"It is a small pool."
Moyes' European experience is not extensive.
He has only guided Everton through four European campaigns and never went beyond the last 16 phase in any competition.
However, Ferguson has never had any doubts his fellow Scot was capable of managing at the very highest level.
And Gill confirmed Ferguson, and Sir Bobby Charlton - who has previously suggested Mourinho was not the type of character would sit easily at Old Trafford - would be asked for their input.
"No-one knows what managing Manchester United is about more than him," Gill said.
"The board will take his counsel and that of Sir Bobby Charlton in order to get the right person to take it forward."
Charlton would be acutely aware of the problems it caused - first for Wilf McGuiness, then Frank O'Farrell - when Sir Matt Busby remained active at Old Trafford following his retirement as manager.
The spectre of Ferguson is going to hang over Old Trafford for a long time.
But Gill is confident the Scot will not be a negative presence.
"Sir Alex will be a great asset to the club," Gill said.
"He will know when he should and should not be involving himself.
"Everyone can rest assured the new manager can get the space and opportunity to do his job without interference.
"Alex will not make that mistake. Of that we can be certain."
As Gill is also departing in the summer, it represents a significant test for new chief executive Ed Woodward.
"Ed Woodward has the opportunity to develop a relationship with the new manager," Gill said.
"I am sure he is capable of doing that for the betterment of Manchester United.
"Alex and I will still be there but on the football club board.
"It is a new era but I am confident the structure we have in place gives a great foundation for that relationship to happen."