The Japan international had been asked about his desire to move back to the Bundesliga but the midfielder told his former manager that he wants to remain at Manchester United.
A knee injury restricted the Japan international to just 17 starts in the Premier League last season following his arrival from Dortmund in June 2012.
Kagawa is currently with United's squad for its tour of Asia and netted in the club's 2-2 draw with Cerezo Osaka on Friday.
Klopp, whose side secured a 4-2 victory over Bayern Munich in the German Supercup on Saturday, says that he contacted the 24-year-old regarding his availability but was told that he wanted to remain at Old Trafford.
"This is not an issue for him this year, not even for us," the BVB coach told Sky.
"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."