Jens Keller's men have lost three of their opening four fixtures and face a struggle to qualify for the Champions League group stage following a 1-1 home draw with PAOK in qualifying.
In the wake of their 2-1 defeat to Hannover on Saturday, the teenager believes it is vital that they add to the squad to rescue their season before it is too late.
"I'm not in the management, but a new player in every part of the team would not hurt us," he told Bild.
S04 travel to Thessaloniki for the second leg of their clash with PAOK on Tuesday and Draxler called on his team-mates to produce a big performance.
"It makes me really angry that we played such bad football in the first half [against H96]. In Thessaloniki there are no more excuses - it's the most important game of the year!"
Schalke, who are 16th in the Bundesliga, have seen a bid for Arsenal forward Lukas Podolski rejected in recent days.
