Macheda has joined Rovers on an initial month's deal.
Giovanni Bia told TMW: "It's been a great choice determined by the desire to get back to playing for the boy. At Manchester United, it was closed and there was no chance to do so.
"So we decided to get out. Doncaster is a friend of Manchester United and needed a striker and so decided to focus on Macheda, who yesterday has already begun with his new team.
"The loan is one month, but can be extended. Now the boy will try to find continuity waiting for January."