Kagawa left Dortmund for United last summer after enjoying a successful two-year spell at Signal Iduna Park.
The Japan international endured a frustrating first season at Old Trafford, struggling to hold down a regular place in the United side due to injuries.
Kagawa has been linked with a move back to Dortmund this summer and Klopp admits he spoke to the playmaker, but that he wants to stay with the Premier League champions.
"This is not an issue for him this year, not even for us," Klopp told Sky Deutschland.
"It was clear relatively quickly, Shinji wants to prevail this year at Manchester United. I did not expect a different answer, you just have to ask even once."