Macheda, who has made just three substitute appearances for United this season, has also been linked with Spanish side Elche as well as Siena and Bologna in his native Italy.
"We have been watching him for a while now," Stuttgart director of sport Fredi Bobic told the Stuttgart Nachrichten newspaper.
"He is one of the players we have on our shortlist."
Macheda's agent Giovanni Bia last week revealed that Stuttgart are favourites to sign the Italian, who was on loan with Queens Park Rangers last season, and has not played a league games for United since December 2011.
"We are at an advanced point with Stuttgart," Bia said.
"Negotiations are going well but he is a player who is liked by a lot of clubs.
"He'll join a club on loan with the option to be signed outright as his contract expires in June 2014."
Bobic has also admitted his club's interest in Colombian forward Duvier Riascos of Tijuana in Mexico, but revealed the deal had stalled.
Bobic said: "It's a pity we are set to be unable to make the deal.
"We still have a glimmer of hope the deal could get back on. Maybe that club is to undergo a change of thinking in that affair. If not, well we definitely have some other arrows back there in our quiver."