The 20-year-old midfielder joined the fellow Bundesliga side from Dortmund at the start of the season, on a deal which could see him stay at the HDI-Arena until June 2017.
However, there is a clause in the contract which offers Klopp the opportunity to re-sign the player at any point during his spell at Hannover.
After struggling to settle at Dortmund, Bittencourt has become a first-team regular at Hannover, scoring four goal in 24 appearances for the club, and Klopp admits he is keeping an eye on the attacking playmaker.
"Leonardo Bittencourt is a player we are keeping tabs on," he told Deutsche Presseagentur.
"He has become very good in front of goal and played a lot of decisive passes at the same time.
"He definitely is now the starlet we recognised when we signed him for Borussia Dortmund from Energie Cottbus. He is a great talent."
Bittencourt features in Tayfun Korkut's squad for their trip to Hoffenheim on Wednesday night and looks set to retain his place on the left flank.