No announcement was made on Monday as to whether Schneider would still be in charge for the relegation battle with Eintracht Braunschweig next weekend, but comments made by the club's director of sport Fredi Bobic on Sunday suggest his reign could be coming to an end.
"I don't want to make any decision out of the emotion I have right now," Bobic told Sky after the 2-1 defeat to Eintracht Frankfurt.
"I need to talk to one or two people, also with Thomas Schneider.
"I'm not ruling anything out. In this kind of job, you can't let your emotions get the better of you."
Schneider led training as usual on Monday, but behind the scenes, Bobic was holding those talks, also with a potential replacement for the under-fire coach.
"I think it's part of my job that I look into different scenarios," Bobic said. "That's totally normal."
Former Hamburg and Basel coach Thorsten Fink's name has been mentioned as a potential replacement with a change still possible before Saturday's meeting with bottom-placed Braunschweig.