Despite speculation that the club has the second-highest wage bill in the Bundesliga behind Bayern Munich, Schalke are currently sixth and seven points off the final Champions League qualification berth.
It is believed that if they were to lose to Swiss side Basel on Wednesday, then Keller could be sacked.
Basel go into the clash at the Veltins-Arena second in the group behind Chelsea and one point better off than Schalke in third.
As a result, avoiding defeat would see Murat Yakin's men advance through to the knockout stages, which would consign their hosts to the Europa League.
Basel also have concerns over Marcelo Diaz due to a muscular complaint that could keep him out of action until the end of December.
Possible starting lineups
Schalke: Fahrmann; Uchida, Fuchs, Howedes, Matip; Neustadter, Boateng, Farfan, Draxler; Szalai, Meyer
Basel: Sommer; Voser, Ivanov, Schar, Xhaka; Stocker, Serey, Frei, Mohamed Salah, Mohamed El Nenny; Streller
Sports Mole says: 2-1