The Japan international looks set for a £5m move to Old Trafford following Dortmund's successful defence of their Bundesliga title.
Kagawa has been integral to the champions' team, scoring 21 goals in 45 league appearances since his move from Cerezo Osaka in 2010.
However, Klopp now seems resigned to losing the attacking midfielder should he not sign a contract extension.
"If Shinji leaves, life goes on," Klopp told Kicker. "After all, it's not like we had planned on playing an identical lineup for the next 25 years."
The 23-year-old has scored nine goals in 29 appearances for his country.