Anderson, known as 'Andow' in Italy, is on-loan at Fiorentina to the season of the season.
"I am sure that lots of players want out," he said.
"Especially people like myself and Nani, who have been in Manchester for seven or eight years.
"Manchester United is a huge club, a club that does everything for its players, but sometimes a footballer wants to leave just to experience a different way to play football and to learn something as well.
"Playing in Manchester was great, it is a prestigious club with a lot of history.
"But I was there for seven or eight years and I want to show Fiorentina my quality and fight for a spot in the starting line-up.
"I thank all Manchester United fans for their love, but I'm here to stay."