The Japanese attacking midfielder returned to Westfalenstadion from Manchester United at the end of the summer transfer window after a failed stint at Old Trafford.
Klopp was hoping to ease Kagawa back into the Bundesliga fray following his return but may be forced to start him in Saturday's home fixture with SC Freiburg after Marco Reus was injured playing for Germany in their opening Euro2016 qualifier against Scotland on Sunday.
"We cannot wait a few more weeks. Shinji is now very important to us," Klopp told Kicker.
"He has impressed in training but will need time to find his form from two years ago."
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