German newspaper Das Bild reports that United boss Sir Alex Ferguson has had scouts watch the 18-year-old in action, but have yet to make an official bid.
Dortmund are reportedly looking for around £20million for the youngster.
Gotze’s agent, Volker Struth, has previously confirmed the interest from Juventusk, AC Milan and Real Madrid in the youngster.
Struth told calciomercato.it: “I heard of the interest from Juventus and AC Milan for Gotze but there are many teams interested.
“There is also Real Madrid and other English and German clubs, but Mario will not move from Dortmund.
“He renewed his contract last month until 2014 and I can assure that he will remain in Borussia again for many seasons.
“We think it’s best for the boy, he is only 18 years old and lives with his parents a few miles from the stadium. His departure is almost impossible.”