The promoted side have endured a difficult return to the Bundesliga, going six league matches without a win and scoring just once during that sequence. Their four goals after eight matchdays represent the division's weakest attacking record, while their midweek 2-0 DFB-Pokal defeat against second-tier Dynamo Dresden added to the pressure.
Sporting director Baumann, who played a significant role in the club's promotion, insists there will be no knee-jerk reaction despite the disappointing start.
"We are not satisfied and we are not underestimating the situation. But after a quarter of the season, we are not going to panic. We have emphasised from day one after promotion that it would be a very difficult season," he told the WAZ.
For Baumann, avoiding relegation would represent an achievement in itself.
"Staying up would be a greater success than promotion," he added.
Schalke supporters are hoping the winter transfer window can provide a solution, particularly after the club made four influential signings ahead of the second half of last season. However, Baumann is not promising another major recruitment drive, with the existing squad expected to improve.
"We will analyse very carefully in the winter, as we do in every transfer window, what the team needs and whether we can improve our squad. But there will be no rushed decisions or knee-jerk reactions. Our immediate focus is on getting better performances out of the players we have. I am convinced that this team can secure survival."
Baumann acknowledged that Schalke must improve in several areas, with the lack of goals an obvious concern. Nevertheless, he remains firmly behind head coach Miron Muslic, whose recent switch to a back four is intended to help the team find greater balance.
"I think he is handling the situation very well. He works meticulously, is clear and open to input. We are absolutely convinced by his work and the path we are taking," Baumann said.
One possible addition is 21-year-old Dursun, who has impressed for Swiss side FC Thun. Schalke are monitoring the Austrian Under-21 international, who has registered 13 goal contributions in 17 competitive appearances this season, according to FussballTransfers.
The 1.90-metre forward is also attracting attention from Union Berlin, with both German clubs having sent scouts to watch him. Dursun is under contract at Thun until 2029, meaning any move would require negotiations with the Swiss club.
Schalke's interest is not yet advanced, but the search for attacking reinforcements reflects the urgency of their situation. Baumann's priority remains improving the current squad, although Dursun is one option the club are keeping under consideration.