The Bundesliga enters the business end of the season this weekend with the penultimate round of matches.
Five sides are battling it out for European qualification while no fewer than four teams are still in danger of following Greuther Furth down into the second division.
Schalke are in pole position to join Bayern Munich, Borussia Dortmund and Bayer Leverkusen in the Champions League, and a win over Stuttgart would seal their place should fifth-placed Eintracht Frankfurt fail to beat Werder Bremen.
"We're already sure of a place in the Europa League, but that's not enough," said Schalke midfielder Jermaine Jones on his club's website.
"We want to get back into the Champions League. That is where we belong.
"We are heading in the right direction, but nothing is decided yet."
Should the Royal Blues fail to pick up maximum points, sixth-placed Freiburg could set up a final-day showdown at their Dreisamstadion by beating Furth.
Yet should either Frankfurt or Freiburg slip up, Hamburg and Borussia Monchengladbach are keen to pounce.
"It is not over yet mathematically," said Hamburg coach Thorsten Fink, who takes his side to Hoffenheim.
Gladbach captain Filip Daems, whose side travel to Mainz with four points to make up on Freiburg and five on Frankfurt, added: "We've got to be there if they slip up."
Things are even tighter at the bottom, although Bremen could end their relegation fears if they manage to end their 11-game winless streak when they face Frankfurt.
For that to be enough, they would still need either Fortuna Dusseldorf or Augsburg to slip up in their games against Nurnberg and Bayern Munich respectively.
Hoffenheim's relegation to the second division could be confirmed if they fail to beat Hamburg and both Augsburg and Fortuna win.
Dortmund travel to Wolfsburg while Leverkusen host a Hannover side who, with a six-point deficit on the top six with two games to play, still have a slender chance of sneaking into Europe.