The Brazil midfielder joined Fiorentina on loan until the end of the season earlier this month, and has no intention of returning in the summer.
Anderson, appearing at a press conference in Florence, insisted he was "here to stay" - and if his words are to be believed, he is not the only player keen on leaving the Premier League champions.
According to the 25-year-old, Portugal winger Nani - who signed a new five-year United contract last summer - is among a host of stars who want to jump ship.
A number of first-team members are out of contract at the end of the season and Anderson believes a large number of them will leave the club.
Question marks hang over the likes of Nemanja Vidic, Patrice Evra and Rio Ferdinand, who all have contracts that are set to expire in July.
There are also doubts over whether Nani and Mexico forward Javier Hernandez will stay at the club.
Anderson told ESPN: "I'm sure that lots of players want out, 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, to learn something as well."