The 50-year-old Moyes, who has spent 11 years at Goodison Park building solid squads on the slimmest of resources, is out of contract with the Merseysiders on June 30.
With only two games left to play this season, and with Everton heading for a commendable top-six finish, Moyes was holding talks with club chairman Bill Kenwright in London late Wednesday.
"He's a winner and has a work ethic similar to Sir Alex," ex-England manager Steve McClaren, and a former assistant to Ferguson at Old Tafford, told the BBC.
"He's also built a dynasty and legacy at Everton. He's waited many years for this opportunity and I hope he gets it."
Moyes and Ferguson have had a close relationship and the Everton manager has long been considered as his fellow Scot's most likely successor.
He was even considered as a possible right-hand man to Ferguson as far back as 2000, when he was in charge at Preston, two years before he took the Everton job.
Existing on a comparatively meagre budget at Goodison Park, Moyes's Everton have not finished outside the top eight since 2006.
He has also been instrumental in nurturing young talent at the club.
Wayne Rooney was handed a league debut by Moyes in 2002 when the striker was just 16.
Two years later, Moyes sold Rooney to Ferguson for £27 million, making him the world's most expensive teenager.
But Everton's lack of financial muscle always proved a stumbling block and the ambitiousMoyes will leave Goodison without a trophy to his name.
Real Madrid manager Jose Mourinho, who established a friendly rivalry with Ferguson while in charge of United's rivals Chelsea, had also been touted for the Old Trafford job.
But Moyes was always the odds-on favourite with all the leading British bookmakers.
Ferguson, 71, guided United to 13 Premier League titles and two European Champions League crowns in 26 years in charge at Old Trafford that yielded an astounding 38 major trophies in total.
Arguably the highlight of his career was the unprecedented Treble of 1999, which included the Premier League, FA Cup and a thrilling come-from-behind win against Bayern Munich in the Champions League final.
Rumours of his retirement only began circulating late on Tuesday, but Ferguson said it was a decision he had been considering for some time.
"The decision to retire is one that I have thought a great deal about and one that I have not taken lightly. It is the right time," Ferguson said.
"It was important to me to leave an organisation in the strongest possible shape and I believe I have done so," added Ferguson, who will bow out with United having wrested back the Premier League title this season from local rivals Manchester City.
Ferguson's final game in charge will be away to West Bromwich Albion on May 19.
United defender Rio Ferdinand praised Ferguson's unmatched commitment to improving the side, telling his Twitter followers: "The bosses (sic) work ethic, his desire to win + to make us better players were unrivalled. Thanks boss."
David Beckham, on United's books as a schoolboy before making his way into the first team, said Ferguson had been like a father to him.
"As I have said many times before the boss wasn't just the greatest and best manager I ever played under, he was also a father figure to me from the moment I arrived at the club at the age of 11 until the day I left," said Beckham, now with French giants Paris Saint-Germain.
There was praise too from an unexpected quarter when Chelsea boss Rafael Benitez, one of Ferguson's bitterest rivals, saluted his old foe.
Ferguson and Benitez often clashed when the Spaniard was coach at Liverpool.
But Benitez, ahead of Chelsea's Premier League match against Tottenham on Wednesday, insisted: "I have always liked to compete against him as a manager.
"As a person, I wish him health in his retirement and I hope he enjoys his football in a different way."
Such has been Ferguson's impact upon United, the club's shares fell by more than four percent in early trading on the US Nasdaq exchange following the announcement of his retirement.
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