While the hosts' quest for a first point continues, Stuttgart are aiming to get their campaign back on track following a home loss last time out.
Match preview
One of five clubs yet to pick up a point in this season's Champions League, Red Star have already lost twice in Belgrade - to Benfica and Barcelona - while suffering four-goal defeats away to Inter Milan and Monaco.
Earlier this month, the Serbian champions were heading towards half time all-square with Barca, but Robert Lewandowski scored the first goal of a brace on 43 minutes, and they ultimately went down 5-2 to their Catalan counterparts.
A record of 16 goals conceded is the worst of any team this term, and with a goal difference of minus 12, it is evident that Crvena Zvezda have struggled to cope with Europe's elite since coming through qualifying.
Two losses have dented a proud record on home turf - which still stands at just six defeats from their last 23 continental contests at the Marakana - but Red Star remain untouchable on the domestic front.
The 1991 European champions claimed their seventh successive league title last term, and they have since won 13 of 14 league games in the current campaign, scoring 44 goals and conceding only eight.
In his second spell at the club, head coach Vladan Milojevic has helped his side stay undefeated throughout their last 36 domestic matches, of which they have won 33, but translating that form onto the main stage has proved beyond them thus far.
Stuttgart were last crowned German champions back in 2007, but they will head into their first-ever game against Red Star having recently re-established themselves among the Bundesliga's elite.
Taking part in UEFA competition for the first time in 11 years, an ambitious squad led by much-admired coach Sebastian Hoeness snatched second place from under the noses of mighty Bayern Munich last season, and they are now challenging for another top-four finish.
However, the Swabians sit just outside the Champions League's playoff places going into the second half of their comeback campaign, after losing their last fixture 2-0 at home to Atalanta BC.
With four points on the board - owing to a 1-1 draw against Sparta Prague and a dramatic 1-0 victory over Juventus - Stuttgart have scored just three goals so far, including one in an opening-day defeat to Real Madrid at the Bernabeu.
After beating Juve in Turin, they will now aim to record consecutive away wins for the very first time in either the European Cup or Champions League, before wrapping the league phase up with games against Young Boys, Slovan Bratislava and Paris Saint-Germain.
Saturday's 2-0 win at home to Bochum leaves Die Roten just adrift of the European places in a tightly-packed Bundesliga table, but to extend this year's Champions League adventure they may need to collect at least six more points.
Red Star Belgrade Champions League form:
L
W
L
L
L
L
Stuttgart Champions League form:
L
D
W
L
Stuttgart form (all competitions):
W
W
D
L
L
W
Team News
Red Star coach Vladan Milojevic has recently welcomed injured trio Ognjen Mimovic, Bruno Duarte and Mirko Ivanic back to training, but it remains to be seen whether they will be ready by Wednesday.
As Saturday's league game against Jedinstva was postponed due to heavy snowfall, the hosts should be well rested following the international break, though Peter Olayinka is expected to miss out due to an Achilles problem.
Senegalese striker Cherif Ndiaye - leading scorer in the league with nine goals - spearheads the hosts' attack, while winger Felicio Milson has found the net in both of his Champions League appearances this term.
Those goals came as a substitute, as Stuttgart-owned Silas has generally been preferred; the DR Congo forward was voted Bundesliga rookie of the season in 2020-21 after scoring 11 goals in 25 games, but he is now out on loan in Belgrade.
Meanwhile, the visitors have several absences to contend with - most notably, up front. The match-winner against Juventus, El Bilal Toure returned from international duty with a broken foot and has undergone surgery, while top scorer Deniz Undav will be out of action until 2025 with a hamstring injury.
Ermedin Demirovic has six goals this season and recently scored for Bosnia-Herzegovina in the UEFA Nations League, so he should deputise for the latter. French playmaker Enzo Millot - who has created more chances from open play (nine) and completed more dribbles (eight) than any of his teammates in this Champions League campaign - is set to support him.
Jamie Leweling (hamstring), Luca Raimund (muscular) and Dan-Axel Zagadou (knee) are still sidelined, but Leonidas Stergiou made his first appearance of the season on Saturday, having finally recovered from a back injury.
Red Star Belgrade possible starting lineup:
M. Ilic; Young-woo, Spajic, Djiga, Rodic; Krunic, Elsnik; Silas, Maksimovic, L. Ilic; Ndiaye
Stuttgart possible starting lineup:
Nubel; Stergiou, Rouault, Chabot, Mittelstadt; Karazor, Stiller; Rieder, Millot, Fuhrich; Demirovic
We say: Red Star Belgrade 1-1 Stuttgart
Neither side has scored many goals so far - averaging under one per game between them - so a tense, close-fought encounter could be on the cards.