Schalke crashed 5-1 at VfB Stuttgart on Saturday, a week after losing the derby match 4-0 against arch-rivals Borussia Dortmund and amid reports that some players had asked the club leadership to get rid of Gross who was only appointed in late December.
Broadcasters Sky and Sport1 as well as Kicker sports magazine said that Gross and Schneider must now go, together with team manager Sascha Riether and fitness coach Werner Leuthard.
Schalke have not confirmed the reports.
The club on Saturday dismissed there had a been a players' "revolt" against Gross. The team then played poorly in Stuttgart, with the Bild paper suggesting that "never has a team played against its coach in such a way."
Schalke are nine points away from safety with just one season win - achieved in January - and nine points overall from 23 games.
Gross, 66, is their fourth coach, following David Wagner, Manuel Baum and brief caretaker Huub Stevens.
