The Manchester United striker, in the final year of his contract, joined the Sky Bet Championship club on an initial month-long deal on Monday and the following evening made his debut for Rovers as a second-half substitute in their 2-1 defeat at Watford.
Macheda, 22, told the Doncaster Free Press: "It would be a shame to just be here for a month. If there is a chance for me to stay until January, it would be great.
"This is the best move for me. It is a good team. We play football and we have what it takes to have a good season.
"I am really happy to be here and I am looking forward to getting more playing time."