The Old Trafford club’s vice-chairman Ed Woodward is leading the search but is drawing on the experience of Sir Alex Ferguson and former chief executive David Gill, who are both board members.
Holland coach Louis van Gaal is the front runner, but sources close to United say he is only one of a list of candidates that has been drawn up.
The club are looking for a coach with a significant level of experience, which means temporary manager Ryan Giggs will not be among those considered.
Van Gaal is on holiday in Portugal, according to reports in Holland, and the 62-year-old will be a free agent after the World Cup. The Dutchman is on the shortlist, along with Real Madrid coach Carlo Ancelotti.
However, former Real Madrid president Ramon Calderon is confident Ancelotti will stay.
He said: “I believe Carlo Ancelotti will be with Real Madrid next season. He’s got a contract. We don’t know what’s happening with Manchester United.
“It’s always a pity when you have to sack a coach. I had that problem with Fabio Capello. Sometimes you have to take those decisions, though. Manchester United’s results have not been normal so it’s a decision they had to take.”
As well as experience, the criteria for the new manager is also thought to include a good grasp of English, which would count against Atletico Madrid’s much-admired Diego Simeone.
United are trying to move on from the controversy surrounding the sacking of Moyes on Tuesday, and Giggs will hold his first news conference as player-manager this morning.
The “Chosen One” banner that has been displayed on the Stretford End since Moyes took over has been taken down, it has been confirmed. It is also understood club chiefs will continue to work hard to line up transfer targets so the deals can be done as soon as the transfer window opens on 1 June. That will also give time for the new manager to indicate his views and wishes on targets.
United have refused to comment on reports owners, the Glazers are due to fly into the UK for talks on the situation.
Meanwhile, West Ham manager Sam Allardyce claimed the process of Moyes’ departure could have been handled better.
He said: “For Manchester United as an institution and a football club as large as they are, the process looked like it was flawed, which was a great shame for Manchester United as a brand and, of course, David Moyes knowing his fate before he was even told.
“That is how it looks from the outside. If that is the case, it is a great shame for David and a great shame Manchester United chose to use that process.”
United have insisted no decision had been taken at the time reports first started emerging.
Roberto Martinez is confident Moyes, his predecessor at Everton, will have no problems in finding a new job. He said: “I am sure he will be ready to get into another job as quick as he can and he won’t have a lack of offers or opportunities, when you have someone who is so hard-working, focused and dedicated in his job.”