The Japan international made the move to the Red Devils from Borussia Dortmund in 2012, before rejoining his former club earlier this summer having failed to make the desired impact in the Premier League.
"I met Sir Alex in Nyon and he's still in love with Shinji," Dortmund boss Klopp told The Sun. "He told me, 'Shame we didn't manage this well so that it worked out for him. We were satisfied in the first year'.
"And in the second year you usually make the next step but he didn't manage to do it. But Sir Alex was saying 'Shame we should have made this work'."
Kagawa scored six goals in 38 league appearances for United.