The Italian forward is due to spend the remainder of the 2012/13 campaign in Germany after agreeing a January switch from United.
"In the winter, the move (to Stuttgart) was only a loan option but I knew there would be a chance to remain at the club after it," Macheda told BILD.
"If Stuttgart want to sign me permanently, I would be very happy.
"Back at Manchester United it was always difficult for me due to the competition for first-team spots.
"It would be great to remain at Stuttgart. Over here the coaches are working with young players and I feel I could progress at this club as a player."