But who should get the job of replacing the most successful manager in British football history?
The hot favourites (Note: Odds correct at 9:30 BST - bookies' quotes are fluctuating continuously)
Jose Mourinho - Evens
Why he should get it: A hugely successful manager in Portugal, England, Italy and Spain, Mourinho has consistently shown that he has outstanding tactical nous, motivational skills and the ability to deal with both prima donnas on the pitch and highly complex club set-ups behind the scenes. What better qualifications could anybody have?
Why he shouldn't get it: His habit of taking big jobs and moving on after two or three years is the exact opposite of what United will want after 26 years of managerial stability.
Will he get it?: A very good chance indeed. Putting aside footballing concerns or the nature of the club, he is quite simply the choice that would make most sense to global stock markets - and that, ultimately, will probably tip the balance in his favour. He also has a good relationship with Ferguson, who is sure to have a big say in the naming of his successor.
David Moyes - Evens
Why he should get it: Years of overachievement at Everton have earned the Scot a stellar reputation for bringing in underrated talent and then getting the best out of them, even clinching Champions League qualification in 2005. He has also shown his long-term dedication - in stark contrast to Mourinho - as he is the third-longest-serving manager in the top flight.
Why he shouldn't get it: There's a huge difference between running a relatively impoverished club and running the world's most valuable sports franchise, and Moyes is completely unproven when it comes to the latter. His constant frustration at Everton's inability to back him with transfer funds also suggests that he is not the man to negotiate the back corridors of Old Trafford - and balance competing interests - with a smile. He has not won a single trophy as a manager since guiding Preston to the League One title (then Division Two) in 2000.
Will he get it?: At first glance he seems the nearest thing to a like-for-like replacement for Ferguson: a straight-talking Scot who commands respect and absolute loyalty, and who could be trusted with a long-term brief to build the side. But Ferguson took over at United only after proving himself a huge success in Scotland, and then had the task of turning a third-rate club back into world beaters. Taking over a club at the top is a totally different matter. In other words, Moyes would have been a good fit for United in 1987, but he probably isn't now.
The other contenders
Jurgen Klopp - 10/1
The Borussia Dortmund coach was strongly linked to the United job just last week, with reports from inside Old Trafford claiming that it was an open secret that Klopp was the "next manager in waiting". He would no doubt jump at the chance: his frustrations at how Dortmund keep on selling his best players - and often to Bayern Munich - would have driven a lesser man to the brink of despair. Instead, Klopp has stayed cheerful and is now 90 minutes away from being a Champions League-winning boss.
Ryan Giggs - 25/1
The Welshman has already dedicated his life so far to the Red Devils, and as a sentimental, fan-friendly choice he would be hugely popular. But giving him control of the team would be like asking a newly-recruited police constable to investigate the assassination of David Cameron. Bringing him in as a coach might make sense - anything else would be unthinkable insanity.
Ole Gunnar Solskjaer - 28/1
The 40-year-old is a United legend and has won back-to-back trophies in Norwegian football with Molde. He has also worked as a coach and reserves manager at Old Trafford, and has the brightest of futures ahead of him - hence the suggestion that he could be a sort of Scandinavian Pep Guardiola at Old Trafford. But his managerial experience so far will count for about as much as a few good seasons playing Championship Manager on his PC when it comes to the men who control United's finances.
Carlo Ancelotti - from 25/1 to 90/1
The Italian has all-but-confirmed that he will leave PSG this summer, and has proven himself a good boss there, with Chelsea and with AC Milan - with whom he won the Champions League twice.
Gary Neville - anywhere from 25/1 to 66/1
Another United legend who has dabbled with coaching roles - not least with England - but his career change to pithy, croaky-voiced pundit is complete enough that he would be seen as a ridiculous choice.
Laurent Blanc - 40/1
The former France manager was once considered among the hot favourites to take over from Ferguson on his retirement, particularly after winning the double in France with Bordeaux in 2009. He failed to set the world alight as France's national team manager, however, with a talent-packed team turning in a string of hugely disappointing performances at Euro 2012. Hard to see him getting a phone call despite the fact that he is available for hire.
Roberto Martinez - 40/1
Earned a good reputation at Swansea and has had Wigan playing well - often brilliantly - in spells. But consistency has been a problem - and the fact that he was publicly turned down by Liverpool last year won't help his chances.
Pep Guardiola - 40/1
Priced up by bookies, but it's impossible to picture the former Barcelona coach going back on his agreement to take over Bayern Munich this summer.
Michael Laudrup - 50/1
The Danish legend has enjoyed a first season at Swansea that is about as good as can be imagined - and has claimed some silverware to boot, with the League Cup. Still relatively new to England and the Premier League, however, and his odds reflect that all he has done so far is keep a good team going well.