The Japan international's future at Borussia Park has been a hot topic in recent weeks, given that he is about to enter the final year of his contract with the club.
"I had a meeting on Monday morning with his agent - Shinji Kagawa told him that he definitely will not extend his contract with us," Zorc is quoted as saying by Revier Sport.
|CROSSING THE DIVIDE?
|66/1||Luis Suarez is 66/1 with Paddy Power to be a Manchester United player on September 1, 2012.|
"Should offers come now for Kagawa, we will deal with them and negotiate."
United have been tipped as front-runners in the race for Kagawa's signature, with manager Sir Alex Ferguson present to watch the 23-year-old grab the opening goal in Dortmund's 5-2 DFB-Pokal final victory over Bayern Munich on Saturday.
It is widely reported that the Bundesliga champions will listen to offers in the region of €15 million (£12m) for the former Cerezo Osaka attacker, who moved to Dortmund in 2010 for €350,000 (£280,000).