A number of former United players have been linked with the job, including Laurent Blanc, Ole Gunnar Solskjaer, Gary Neville and even the currently active Ryan Giggs (all listed in Paddy Power odds via Daily Mail).
Of those choices, Blanc would make the most sense. The 47-year-old played briefly for United near the end of his career and has experience managing Bordeaux and the French national team. He is not currently managing a team.
Solskjaer, 40, scored a famous goal for United in the 1999 Champions League final and went into management with the club's reserves in 2008. Since 2011, he has managed Molde in his native Norway, winning two league titles.
Neville has served as an assistant to England manager Roy Hodgson since 2012. Giggs is still active as a player.