The Italian has failed to establish himself in the United first team squad after unsuccessful loan spells at Sampdoria and QPR and Stuttgart are in the market for a striker.
"We have been watching him for a while now," Bobic told the Stuttgart Nachrichten newspaper. "He is one of the players we have on our shortlist."
Stuttgart's 2-0 defeat to Wolfsburg at the weekend underlined their need for a striker with top scorer Vedad Ibisevic suspended and his replacement Shinji Okazaki failing to impress.
"We know how very important Vedo is for us, but we are not dependent on him," said Bobic.