The reigning European champions had been linked with the Schalke attacker, but Karl-Heinz Rummenigge says they will only sign players who provide more quality "immediately"
The Gunners had been close to signing the 20-year-old in January, having sent a delegation to Germany to negotiate a deal, but looked less likely to acquire the playmaker after he refused to rule out a move to the Allianz Arena.
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"I can assure that we will not buy Julian Draxler this summer," the 58-year-old told Welt am Sonntag.
"I do not know [if he wants to join Bayern]. We never talked to his agents. In my opinion the public do not understand our transfer policy yet.
"We will not buy any players from Dortmund or Schalke only to hurt them. We will buy only players who bring more quality to the club immediately.
"In the past we bought some players to be better prepared for the future because some of our players were becoming older than 30. But we will not do that anymore."