Roberto Di Matteo's men have won only four league games in 2015, leaving them in danger of losing out on a spot in the Europa League next season - prompting the pair and Marco Hoger to be suspended.
The 2-0 reverse at RheinEnergieStadion secured Koln's top-flight status and left Schalke 13 points behind fourth-placed Bayer Leverkusen.
General manager Horst Heldt - who has reportedly held a crisis meeting with Di Matteo - said after the game: "Some players are - regardless of contractual arrangements - going to feel the consequences."
Schalke announced that Boateng and Sam will not be welcomed back at the Veltins Arena, but remain under contract with the Gelsenkirchen side. The pair are allowed to talk to other clubs to negotiate a summer move.
Hoger, though, is suspended and can return to the club on Sunday for a second chance to prove his worth.
"There is no relationship or trust with Kevin-Prince Boateng and Sam anymore," Heldt told reporters. "We are not convinced that either player can help us in the last two games of the season.
"With Hoger we have doubts about his loyalty to the club. He will get a chance now to think about it this week and then we will have a talk where we will discuss whether it makes sense to keep working together.
"I have informed the players that the first goal is to finish in a Europa League spot after a consultation with Di Matteo."