United have been beaten on two of their previous three visits to Norwich, in 2005 and 2012, but will be desperate to claim maximum points this time around as they seek to make up ground on the Premier League pacesetters.
After a poor start to the campaign, last season's champions have recorded five straight wins in all competitions, but remain outside the top four.
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The sides have met twice at Old Trafford this year, with March's league meeting followed by a League Cup tie in October, and United ran out 4-0 victors on each occasion.
Javier Hernandez scored two goals in the most recent win over Norwich and will be hopeful of getting another chance to impress in the continued absence of Robin van Persie.
The last league game between United and Norwich, in March, saw Shinji Kagawa claim a hat-trick.
However, the Japan international has made less of an impact since Moyes replaced Sir Alex Ferguson as manager, starting just five league games.
Norwich have found goals hard to come by throughout the season, scoring just 16 in 18 league games.
Only three players have contributed more than one goal for Chris Hughton's men thus far and Gary Hooper is the club's top scorer with five.
Norwich saw a four-game unbeaten run at home come to a shuddering halt on Boxing Day as Scott Parker scored a late winner in a 2-1 victory for Fulham.
United will be without the services of Phil Jones, who has been ruled out for a fortnight with a knee injury, while Rafael could be a doubt after limping off with a groin problem on Thursday. Van Persie (thigh) is also among those unlikely to feature through injury and Antonio Valencia is suspended after he was sent off against Hull.
Michael Carrick could make his first start since the end of autumn, however, after coming on as a substitute on Boxing Day.
Norwich, meanwhile, have Michael Turner out through suspension, while Jonny Howson (back) is reported to be facing a late fitness test.