It appears that the current Everton boss is the frontrunner for the role, but is he the right man to carry on Ferguson's work?
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The case in favour of Moyes, presented by Mark Langshaw
David Moyes has done a phenomenal job during his 11-year stint at Everton, transforming the Merseysiders from a club rooted in the lower reaches of the Premier League to regular European contenders, a feat he achieved on a shoestring budget.
Manchester United would be taking something of a risk by appointing him as Alex Ferguson's successor considering he has never lifted silverware during his Everton career - but it's a gamble that would ultimately pay off.
Moyes would certainly have a point to prove after taking up the Old Trafford hotseat, but he made a significant step up in his managerial career when he joined Everton from Preston North End in 2002, and he rose to that challenge admirably.
Although the 50-year-old lacks European pedigree, he has a proven track record of getting the best out of the players at his disposal, not to mention being shrewd in the transfer market.
The task at hand at United would be very different to the one he encountered when he took the reins at Goodison Park - capturing the biggest-name players and maintaining the club's position as one of the biggest and best in the world - but there's no evidence to suggest that he won't meet this challenge with the same degree of success.
In many ways, the Scot is a natural successor to Ferguson, sharing numerous qualities with his compatriot. As a strict disciplinarian and master of man-management, Moyes is one of the few men capable of filling the considerable shoes of United's legendary boss.
After more than a decade in charge at Everton, many believe that Moyes has taken the club as far as he ever will and is now ready for the next challenge; and while trophies have eluded him during his tenure, he can leave Goodison with his head held high.
The case against Moyes, presented by Liam Apicella
Let me start by saying that David Moyes is a very, very good manager who has done a remarkable job at Everton. As Mark says, he inherited a club that was more used to fighting against relegation and he would leave them in a much stronger position.
But surely following someone such as Sir Alex Ferguson requires a manager that has been there, done that and got the T-shirt? Someone that has battled it out for league titles on a regular basis.
Moyes also has a poor record against the so-called 'Big Four' since he took over at Goodison. From 45 trips to Anfield, Old Trafford, the Emirates and Stamford Bridge - Everton have won... none! Zero, zilch. That really is not good enough considering the players and teams that Everton have had down the years. Those are the sort of grounds that United need to win at on a regular basis.
What's more, United have aspirations to win the Champions League - a competition in which Moyes has limited experience (Everton lost a qualifying encounter against Villarreal in 2005). Ferguson himself took several years to adapt tactically to the tournament. United fans will remember defeats to the likes of Gothenburg and Monaco and shudder. Can the club afford a spell where they are no longer a force in Europe?
Then we come to the transfer market. Through no fault of his own, Moyes is not used to spending the big bucks. As Mark quite rightly points out, he has been "shrewd" by signing the likes of Phil Jagielka, Tim Cahill and Kevin Mirallas to name three. How will he cope when it comes to bidding for that £20m or £30m player. And at that price, what is his judgement like?
Furthermore, players like Robert Lewandowski and Gareth Bale have been linked with United of late. Can Moyes attract and convince that sort of quality to join in the way that Ferguson may have? Or Jose Mourinho? Or Jupp Heynckes? Lest we forget, Fergie somehow convinced Robin van Persie to turn down Manchester City last summer.
This is by no means a piece aimed to dig at Moyes - as mentioned in the introduction he has transformed Everton. But his appointment would be a gamble and following such a long period of success, that is something United cannot afford to do. They only have to look down the road at rivals Liverpool to see that.