Westhauser was accompanied by two others when he fell on Sunday in the Riesending caves near Berchtesgaden, Bavaria.
He reportedly sustained injuries to his upper body and head although by Tuesday, Chiemgau Mountain Rescue spokesman reported that Westhauser was responsive and able to stand for short periods of time.
200 people are involved in the rescue operation, with hope the man will be extricated by the end of the week.
Westhauser was among the first to discover the cave system years ago and works as a cave researcher for the physics department at the Karlsruhe Institute of Technology. The institute issued a statement expressing "hope that the rescue operation can soon come to a successful conclusion" and that "We wish him a quick and complete recovery."