Rangnick's side won 1-0 at home to Crystal Palace last weekend to move up to sixth in the table.
They will now make the trip to Norwich with Dean Smith and co at the foot of the table.
The Canaries lost 3-0 to Tottenham last time out and are in desperate need of points going into the festive period.
But United have a great record against Norwich having won eight of their last nine meetings.
Norwich v Man United: talkSPORT commentary
The Premier League clash is set to take place on September, December 11 at Carrow Road and kick-off is scheduled for 5:30pm.
Lynsey Hipgrave will be your host while commentary will be provided by Sam Matterface and former England defender Alvin Martin.
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Norwich v Man United: Team news
Mathias Normann could return for Norwich but Milot Rashica remains out.
Todd Cantwell is back after a COVID-related absence.
Brandon Williams is ineligible to face his parent club while Sam Byram and Christoph Zimmermann won't feature again.
Aaron Wan-Bissaka is a doubt but Luke Shaw could return to league action.
Anthony Martial could miss out and Edinson Cavani, Paul Pogba and Raphael Varane remain on the sidelines.
Norwich v Man United: Match facts
Norwich have lost eight of their last 10 Premier League meetings with Man Utd (W2), including the last three in a row. It's the fourth time they've lost three consecutive Premier League games against Man Utd, but they've never lost four in a row against them in the competition.
None of Manchester United's last 14 away league games against Norwich has finished level, with the Red Devils winning nine of these (L5).
Manchester United are winless in their last four Premier League matches against newly promoted sides (D3 L1), losing 4-1 to Watford earlier this season. The Red Devils haven't gone five league games in a row without a win against such sides since a run of seven between January 1992 and January 1993.
Two of Norwich's last four home Premier League matches have ended goalless, one more than in their previous 47 at Carrow Road. The Canaries' two clean sheets in four home games is also as many as they managed in their previous 26 in the top-flight.
Norwich have failed to score in a league-high nine different Premier League games this season, while their eight goals scored is their fewest after 15 games in their league history. Of the 17 previous clubs to have netted eight goals or fewer after 15 top-flight games, only three have avoided relegation - Sheffield United (1990-91), Everton (2005-06) and Crystal Palace (2017-18).
After an English-league record 29 consecutive away games unbeaten, Manchester United have now lost two of their last four on the road, conceding four goals in both defeats.
Man Utd's Marcus Rashford has been involved in four goals in his two Premier League games against Norwich (3 goals, 1 assist), averaging a goal involvement every 37 minutes against the Canaries in the competition.
This will be Ralf Rangnick's first away league match in charge of Manchester United - none of the previous four permanent Man Utd managers have lost their first league game on the road (W3 D1), with Alex Ferguson the last to do so (2-0 at Oxford United in November 1986).
Norwich's Dean Smith has already beaten Manchester United once in the Premier League this season, winning 1-0 with Aston Villa in September. He could become the first manager since Andy Aitken in 1908-09 to beat Man Utd with two different clubs within the same top-flight season - Aitken won 5-0 with Middlesbrough and 3-2 with Leicester that season.
Three of Mason Greenwood's four Premier League goals this season have come away from home, making him Manchester United's highest league goalscorer away from Old Trafford this season.