The 19-year-old is one of the hottest young properties in Europe having shined for Dortmund since breaking into the first team in 2009.
Gotze, already capped 12 times for Germany, is expected to play an integral role in his country's Euro 2012 campaign this summer.
His agent, Dirk Hebel, claims several of Europe's top clubs are chasing the attacking midfielder, who has not featured for Dortmund since December 11th due to a groin injury.
Hebel named United and Juve as two suitors who have been in touch over Gotze but insists the Bundesliga club will not let him leave for less than €40million (£33m).
The agent told calciomercato.com: "I think in Europe all the top clubs are interested in Mario.
"I can confirm that I have had contact with Juventus and Manchester United, but not only them.
"I don't know if he'll go away after this season, you should ask the Borussia. But I think that they will not let him leave for less than 40 million euros.
"He still is very happy at Dortmund, though now he is injured."