The Royal Blues take a three-point cushion over fifth-placed Eintracht Frankfurt into their final two games of the season, knowing a win this weekend could seal fourth position and a Champions League play-off place.
"The lads are all motivated to play in the Champions League next season," Schalke midfielder Jermaine Jones said.
"We are now playing at home against Stuttgart and of course we want to defend fourth place.
"We're already certain of a place in the Europa League, but that's not enough for us. We want to get into the Champions League again - that's where we belong."
Stuttgart are also assured a place in the Europa League having reached the final of the DFB-Pokal, where they will play champions Bayern Munich.
That means they will be under little pressure on Saturday and can just enjoy themselves at the Arena AufSchalke.
"They have nothing to lose," Jones said on his club's website. "Their highlight of the season is the cup final.
"They have a good team and they showed that in the reverse fixture."
Stuttgart's focus goes beyond the cup final in Berlin on June 1, though, as they are already planning for next season, having confirmed the signings of Konstantin Rausch from Bundesliga rivals Hannover, Daniel Schwaab from Bayer Leverkusen and Marco Rojas from Melbourne Victory.
"Marco has just been named Australia's player of the year, but that is not the only reason we wanted him," Stuttgart's director of sport Fredi Bobic said.
"He is a versatile attacker with a stunning turn of pace."