Jose Mourinho's side have already secured their place in the last 16 of the competition at the expense of their Spanish opponents, but could progress as group winners if they win and Juventus fail to beat Young Boys.
Valencia go into Wednesday's match already knowing their fate, with the Europa League awaiting them in the New Year.
Marcelino's side have won just one of their five group games so far this season, with that coming at home against tournament debutants Young Boys last month.
Juventus are the only team to have beaten Valencia in Group H, though, and it was their 2-0 triumph at the Mestalla on matchday one which has proven to be particularly costly for Valencia, who failed to make the most of Cristiano Ronaldo's first-half red card.
Away draws to United and Young Boys followed before beating the Swiss outfit, but another defeat to Juve - this time in Turin - brought an end to their hopes of reaching the knockout rounds last time out.
It is now just one win in their last eight Champions League outings, and Valencia have failed to even score in six of those games, with the matches home and away against Young Boys being the only exceptions in that drought.
The win over Young Boys is one of only two games Valencia have won at home in their last six such Champions League outings, losing the remaining four of those.
Los Che also ended up dropping into the Europa League during their last Champions League appearance in 2015-16, when they finished third before hammering Rapid Vienna 10-0 on aggregate in the last 32 and then losing to Athletic Bilbao in the next round.
It may be that Europa League success is Valencia's most likely route back into the Champions League next season, though, as they currently sit 15th in La Liga and eight points adrift of the top four.
The vast majority of those dropped points have come from draws, though, with Valencia having incredibly shared the spoils nine times from their 15 league games, winning just three games and also losing only three - two fewer than Real Madrid and the joint-third lowest tally of defeats in the league.
Eight of those nine draws came in their opening 10 league games, but the latest came as recently as Saturday as they held title-chasing Sevilla to a 1-1 draw at the Mestalla courtesy of Mouctar Diakhaby's late equaliser.
Recent Champions League form: LDDWL
Recent form (all competitions): WWLLWD
It is not often that Manchester United have been able to approach matches with a relatively carefree attitude this season, but the pressure is temporarily off their shoulders for this one.
Qualification for the last 16 is already secured, and the mood around the club was lifted further by a display of rare attacking excitement as they cruised to a 4-1 victory over Fulham on Saturday.
United had failed to win any of their three previous Premier League games prior to that triumph, but the result lifted them back up to sixth place and keeps them in the race for a top-four spot this season.
The Red Devils' only win in the month prior to that Fulham victory came against Young Boys in this competition, but even that was far from convincing as United needed Marouane Fellaini's 91st-minute winner to scrape past the Swiss minnows.
It was enough to secure a place in the knockout rounds with a game to spare, though, and Mourinho's side will now be looking to sign off from the group stages with a third successive away win.
A trip to the Mestalla looks easier than United's most recent away Champions League outing - a famous 2-1 victory over Juventus - and the Red Devils have now lost just one of their last 11 European matches on the road.
United have also only lost one of their last nine visits to Spain, although their general record against La Liga opposition has not been very good in recent years, winning only two of their last 14 such meetings.
Should they improve that record on Wednesday then they could register back-to-back wins for the first time since that trip to Turin more than a month ago, and could even pip Juventus to top spot in the group.
Doing so would require the Serie A champions to drop points in Switzerland, though, and Mourinho will be content enough to settle for second place having seen that prospect come under threat after only one win in their first three group games.
Recent Champions League form: WDLWW
Recent form (all competitions): LDWDDW
Mourinho has already confirmed that Paul Pogba will start against Valencia, having only made the bench for United's last two games.
Kevin Gameiro and Jeison Murillo are doubts due to adductor and ankle injuries respectively, but the likes of Michy Batshuayi, Denis Cheryshev and Geoffrey Kondogbia are all available to return to the starting XI.
Valencia possible starting lineup:
Neto; Wass, Garay, Diakhaby, Gaya; Soler, Kondogbia, Parejo, Guedes; Batshuayi, Moreno
Man Utd possible starting lineup:
Romero; Dalot, Bailly, Jones, Young; Pereira, McTominay, Pogba; Mata, Lukaku, Rashford
Head To Head
Five of the last six meetings between these two sides - and six of nine overall - have ended in a draw, including the reverse fixture at Old Trafford.
United did win on their most recent visit to the Mestalla, though, when Javier Hernandez got the only goal of the game during the 2010-11 group stages.
Valencia have only ever beaten United once - in the 1982-83 UEFA Cup first round - but the Red Devils have kept a clean sheet on all of their previous three Champions League visits to the Mestalla.
We say: Valencia 1-1 Man Utd
Barring a shock result in Switzerland, these two only have pride to play for in this match. United will make changes and so will not be at full strength, but they should still have enough to come away from Spain with something.