Serie A and La Liga sides are also said to be interested in the Italian, whose contract expries in June 2014, but the German club are in pole position to sign the 21-year-old.
"We are at an advanced point with Stuttgart," Giovanni Bia told TMW. "Negotiations are going well.
"He is a player who is liked by a lot of clubs. Two Spanish ones, for example, are looking to intervene.
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"He'll join a club on loan with the option to be signed outright as his contract expires in June 2014."
Macheda joined United in 2008 and played a memorable role in their 2008-09 Premier League title-winning season, scoring an injury time winner against Aston Villa, and has gone on subsequent loan spells to Sampdoria and QPR.