Watzke's claims come after the Japan international revealed to a local TV station that he was disappointed with his debut season in England, and would be open to a return to Dortmund in the future.
The attacking midfielder was frustrated by injuries and a lack of regular first-team football in his debut campaign in the Premier League, leading to speculation he is unsettled and a return to the Bundesliga could be on the cards.
"Shinji (Kagawa) is a player we would welcome back," Watzke told BILD. "The door is always for him at our club."
But Watzke knows that the chances of the 24-year-old making a sensational return are unlikely after just one season in the Premier League.
Boss David Moyes has spoken of his excitement at the opportunity of working with the gifted Kagawa, and former Dortmund midfielder Thomas Kroth admitted the new United boss is unlikely to part with his promising midfielder.
"I believe Shinji Kagawa will be staying on at Manchester United," Kroth added.
"But football is a fast business, you never know."