The Japan international, who has been heavily linked with a move to Old Trafford, has rejected an extension and now seems certain to leave the Westfalenstadion in the summer
The Japan international's current contract with the Bundesliga titleholders expires at the end of next season and the club have apparently offered to double his wages in order to remain at the Westfalenstadion until 2016.
However, Zorc has admitted that attacking midfielder Kagawa is not interested in extending his stay in Dortmund and has his heart set on a switch to the Premier League.
"Last week I held talks with Shinji and his advisers," the former Germany international told Sky90. "To date, he is not willing to extend his contract with Borussia Dortmund.
"He has a specific career plan and that involves playing in England. It must be accepted, but it is not good [for the club]."
While Zorc is seemingly resigned to losing Kagawa, who has emerged as one of United's principal summer transfer targets, the Dortmund legend is confident of holding on to top scorer Robert Lewandowski.
"I assume that Lewandowski will still be playing for us for the next two years," the 49-year-old said of the Poland international.
Both Kagawa and Lewandowski played a key role in Dortmund retaining their German crown this season.