The talented 21-year-old is said to have attracted interest from several European heavyweights, with Old Trafford supremo Sir Alex Ferguson believed to be an admirer.
It was thought that the Red Devils were willing to offer a significant sum in order to secure the services of Kagawa, but Dortmund are not looking to sell the Japanese international.
Dortmund’s general manager, Michael Zorc, claims that the club are more focused on agreeing a new deal for the player rather than cashing in on him.
"Shinji is contracted to our club on a deal until June 2013," he said. "We have the desire to strike a long-term deal with Shinji and we are not going to panic just because Manchester United have reportedly expressed an interest.
"We are going to meet with his agent very soon and we will sit down and negotiate a contract extension.
"Shinji has excellent pace, great technique and he scores regularly. To have scored eight goals and assisted one so far this season is a great return."
The fact that Kagawa is currently away on international duty at the Asian Cup could scupper any possible move during the January transfer window, but Ferguson could rekindle his interest come the summer.
Kagawa has been tipped to join United as uncertainty surrounds the future of Old Trafford stalwart Paul Scholes, who could leave the Red Devils at the end of the current campaign.
NEWS:Kagawa ruled out of Asian Cup final
By Elliott Binks
