The 19-year-old goalkeeper moved between the two Bundesliga clubs in the summer to plug a gap caused by an injury to Leverkusen's Rene Adler, and is due to return to Stuttgart at the end of his loan spell early next year.
His performances for Leverkusen may well have convinced them to try to sign him on a permanent deal, but Labbadia would not like to see that happen.
"At the moment, we have the agreement that Leno will stay in Leverkusen until the winter and then he will come back," Labbadia told Sport1 television.
"I would definitely like to keep hold of him."
Leno would then rival Sven Ulreich for the role of first-choice keeper for Stuttgart, and Labbadia says that would be a welcome scenario.
"We would have an excellent situation in terms of goalkeepers," he said.
"When Bernd comes back, of course we want to intensify the battle for places."
Labbadia already has good experience of what an intense battle for the number one jersey can achieve.
Shortly after taking over as coach last season, he dropped Ulreich for an important Europa League fixture with Marc Ziegler preferred.
Although Ziegler was injured in that game and did not return at all that season, Ulreich's form improved substantially and he made numerous important saves to help the club avoid relegation.