The Scot has been nominated along with Manchester City manager Manuel Pellegrini, who went unbeaten in December, Chelsea's Jose Mourinho and Everton's Roberto Martinez.
Chelsea had five wins from seven games, one draw and a defeat while Martinez, who replaced Moyes at Everton, led his side to four wins from six matches, one draw and one defeat.
United started December with a 2-2 draw against Tottenham before subsequent 1-0 home defeats to Everton and Newcastle.
A run of four wins followed, against Aston Villa, West Ham, Hull and Norwich, before United lost 2-1 at home to Tottenham on New Year's Day.
Swansea knocked United out of the FA Cup on Sunday before Sunderland beat them 2-1 in the first leg of their League Cup semi-final.
It is the first time since 2001 that United have lost three games in a row.
(Reporting By Tony Goodson, editing by Pritha Sarkar)
