Leverkusen’s first-choice Rene Adler is set to be out for several months with a knee injury.
Adler’s replacement Fabian Giefer sustained a concussion towards the end of the 2-0 defeat to Mainz at the weekend.
Leverkusen are now looking to bring in Leno on a short-term deal.
“We are looking at Leno,” Holzhauser told Sky Deutschland. “Whether we bring him in depends also on Stuttgart.”