Germany’s Bild newspaper reported that Baumgartner entered the airport’s airspace last week, without permission, and flew below the minimum height of 700 metres.
He did not respond to radio calls to abort his flight. He then changed his course and flew towards Salzburg, with a Bavarian police helicopter in pursuit.
German Air Traffic Control confirmed that there was a corresponding incident. "There was a helicopter flying through the control zone, possibly without approval, which is currently under investigation," a spokeswoman said.
Bild reported that Baumgartner could even have his license taken away.
Baumgartner has said he would like to fly rescue helicopters once his career as a skydiver is over.
He made history in 2012 by breaking the world record for the highest-ever skydive, jumping from a balloon more than 39km (128,000 ft) up in the stratosphere.