Leipzig need Bayern Munich to drop points at Mainz 05, otherwise the Bavarians will seal a ninth successive title, while Stuttgart will be hoping for Freiburg to drop points to keep the top half of the table open this weekend.
Indeed, Leipzig saw their lingering title hopes all but come to an end after losing 2-1 to struggling FC Koln on Tuesday.
Amadou Haidara levelled proceedings moments before the hour mar with a superb strike from outside of the area, but Hector was not to be denied being the matchwinner, latching onto Ondrej Duda's clever back-heel before clinically scoring his first ever Bundesliga brace.
Should Bayern win against Mainz on Saturday, Leipzig's dreams of winning their first ever title will come to an end for another campaign, but Nagelsmann will likely console himself and his players with the fact that they remain in the DFB-Pokal, which the club has never won either.
Stuttgart, meanwhile, lost their fourth game in their last five matches with a disappointing 3-1 loss at home to high-flying Wolfsburg.
Pellegrino Matarazzo's side certainly had their fair share of chances, with Sasa Kalajdzic firing straight at Koen Casteels having been played through on goal, before Philipp Forster missed a penalty - and the ensuing rebound - after John Brooks had handled the ball inside the penalty area.
However, the Wolves showed the efficiency which has seen them rise to third in the table this season, with Xaver Schlager powering in the opener from range, before Josip Brekalo crossed for Wout Weghorst to head home his 20th league goal of the campaign and double his side's lead heading into the break.
Matarazzo's side will still hope to finish in the top half of the table, though, which would be a fine achievement considering this is their first season back in the Bundesliga after only gaining promotion last season.
Leipzig will remain without Dominik Szoboszlai and Konrad Laimer due to their groin and knee injuries respectively, but both will be hoping to be involved in next weekend's cup semi-final against Werder Bremen.
Yussuf Poulsen is also likely to miss out again due to his thigh issue, with Alexander Sorloth handed another opportunity to lead the line.
Angelino was only used from the substitutes' bench during the defeat to Koln as the left-back continues in his recovery from a long-term muscle injury, but he should come back into the starting XI, with Nagelsmann perhaps reverting to his favoured back-five system.
Wamangituka could be out until November due to an ACL injury, but Gonzalez should be fit to return from his thigh injury in time for Stuttgart's next match against Augsburg in two weeks' time.
The same applies for Lilian Egloff, who is close to recovering from an ankle injury, but Borna Sosa and Orel Mangala face a race against time to feature again this season, while Marcin Kaminski is out due to COVID-19.
Castro is likely to replace 19-year-old Naouirou Ahamada in midfield, while Erik Thommy could come into the side for Roberto Massimo in order to allow Tanguy Coulibaly to switch to his natural right side.
RB Leipzig possible starting lineup:
Gulacsi; Orban, Upamecano, Halstenberg; Mukiele, Kampl, Sabitzer, Angelino; Olmo, Nkunku; Sorloth
Stuttgart possible starting lineup:
Kobel; Mavropanos, Anton, Kempf; Coulibaly, Endo, Castro, Thommy; Forster, Klimowicz; Kalajdzic
We say: RB Leipzig 2-1 Stuttgart
We expect Leipzig to bounce back with a win against Stuttgart, who understandably seem to be struggling without Wamangituka and Gonzalez providing foils for Kalajdzic in attack.
Leipzig have still played some excellent football despite their poor results of late, too, and will be looking to rebuild confidence ahead of next Friday's DFB-Pokal semi-final against Bremen.