The English giants are level on nine points with both Leipzig and Paris Saint-Germain in a fascinating Group H and need to avoid defeat at the Red Bull Arena in order to progress to the knockout round.
Leipzig impressively reached the semi-finals of last season's Champions League before losing to French giants PSG, but they are extremely inexperienced at this level of football - currently competing in just their third group-stage campaign.
Leipzig managed to recover with a 2-1 home win over PSG but then lost the reverse game in Paris to leave themselves in a difficult position in the section ahead of their away game with Basaksehir last week.
The Turkish giants levelled the scores at 3-3 in the latter stages of the clash in Istanbul, but a 92nd-minute winner from Alexander Sorloth moved Nagelsmann's team onto nine points.
The Red Bulls, who played out an entertaining 3-3 draw with Bayern Munich in the Bundesliga on Saturday, would qualify for the knockout round if they beat United on Tuesday, although a draw would also be enough if PSG lost to Basaksehir in the section's other match.
United were in an excellent position in the group after matchday two, with back-to-back wins over PSG and Leipzig seeing them firmly take charge of the section. A damaging 2-1 loss in Istanbul followed, though, and now Solskjaer's team are sweating on a spot in the round of 16.
The Red Devils did manage to return to winning ways at home to Basaksehir on November 24, but a 3-1 home defeat to PSG last week means that they have work to do in order to advance to the knockout round.
As mentioned, the 20-time English champions will go through if they avoid defeat in Germany, while they will finish first if they secure a point and PSG do not manage to overcome Basaksehir.
Solskjaer's team have won four of their last five matches in all competitions, including a morale-boosting 3-1 victory over West Ham United in the Premier League on Saturday, when they again had to come from behind.
United have a huge game at home to Manchester City in the Premier League next weekend but simply cannot afford to look past Tuesday's clash as they attempt to book their spot in the knockout round of Europe's premier competition for the 19th time.
RB Leipzig Champions League form: LWLWLW
RB Leipzig form (all competitions): WDLWWD
Manchester United Champions League form: LWWLWL
Manchester United form (all competitions): WWWWLW
Leipzig will again be without the services of Lukas Klostermann, Fabrice Hartmann, Konrad Laimer, Benjamin Henrichs and Hwang Hee-chan on Tuesday night, but the team did not pick up any fresh concerns against Bayern.
Ibrahima Konate, who continues to be linked with a move away from the Bundesliga club, should line up in the middle of the defence once again, but there will be no Dayot Upamecano, with the Frenchman missing out through suspension.
Fred is suspended following his red card against PSG last week, meaning that Paul Pogba could keep his spot alongside Scott McTominay in midfield, with Alex Telles and Aaron Wan-Bissaka in the wing-back areas as Luke Shaw is still not fully fit following a hamstring issue.
David de Gea missed out with a slight knee issue against West Ham but should be back in the side for this match. Both Anthony Martial and Edinson Cavani are huge doubts, though, with the pair both picking up muscular injuries in the 3-1 victory over the Hammers.
RB Leipzig possible starting lineup:
Gulacsi; Mukiele, Konate, Orban, Angelino; Sabitzer, Kampl; Haidara, Forsberg, Olmo; Poulsen
Manchester United possible starting lineup:
De Gea; Lindelof, Maguire, Tuanzebe; Wan-Bissaka, McTominay, Pogba, Telles; Fernandes; Greenwood, Rashford
We say: RB Leipzig 2-2 Manchester United
United only need a point to progress to the knockout stage, and we fancy the English giants to have enough to advance. Leipzig have conceded six goals in their last two matches, and Solskjaer's side are certainly capable of harming the Bundesliga outfit, as they demonstrated at Old Trafford in the reverse game.