The Brazilian, who joined Fiorentina on loan during the January transfer window, has warned that some of the current squad may want out in a search for a new challenge.
Anderson, who arrived in Manchester from Porto seven years ago, failed to earn regular game time under new manager David Moyes with United struggling in their attempts to defend their Premier League title.
Although he is yet to taste victory as a Fiorentina player, Anderson hopes to move to Sere A permanently, expecting others to also eye an exit from United.
"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."
