Anderson joined Fiorentina on loan until the end of the season earlier this month, and the midfielder has no intention of returning in the summer.
The Brazilian, 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 Barclays Premier League champions.
Nani only signed a new five-year contract last summer, but is among a host of players who want to jump ship, according to Anderson.
"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," Anderson was quoted as saying by ESPN.
"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."
There is an inescapable feeling that United's squad needs a huge revamp in the summer.
Rio Ferdinand's contract expires at the end of the season, and given his lack of playing time this term, it would appear unlikely that he will renew his current deal.
Patrice Evra and Nemanja Vidic are coming towards the end of their contracts while question marks also hang over the likes of Nani and Javier Hernandez.
Six months after failing to land some of his main targets, manager David Moyes belatedly boosted his playing squad by signing Juan Mata for a club-record £37.1million.
The Spaniard has enjoyed an encouraging start to life at Old Trafford, but he was unable to help the team avoid an eighth defeat of the season at Stoke on Saturday.
United were the victims of misfortune when Charlie Adam's free-kick flew past David De Gea off the foot of Michael Carrick, but Mata knows time is running out for the Red Devils, who sit seven points off fourth place.
"We went back home (from Stoke) with no points, feeling that we just can't lose this kind of game again," Mata wrote on his personal blog.
"I hope that piece of luck we are missing will come to our side, because we are struggling even with injuries."
Mata's arrival at United was like something out of a Hollywood blockbuster, and the early signs are that the Spaniard will be more of a hit with United fans than a miss.
The 25-year-old enjoyed a successful debut in the win against Cardiff and he set up Robin van Persie for his goal versus Stoke.
Despite ending up on the losing side at the Britannia Stadium, Mata has seen enough over what he describes as a "very intense" week for him to believe that United can upset the odds and end the season in the top four.
"I'm sure we will start a good streak and get better results," Mata said.
"We all hope to climb up in the table.
"The week started with a victory against Cardiff. It was my first game with United, and it was in Old Trafford.
"I can assure you that I will never forget that night. The reception from the fans was unbelievable. And the ovation when I was substituted, amazing. You get goose bumps.
"Unfortunately, we didn't win in Stoke.
"It's a tricky stadium, and the wind was not a good help to play football, but I honestly think that we didn't deserve to lose.
"I am very positive about the rest of the season; the team's mentality is not in doubt."
Mata feels he has settled in well, but there is one vital ingredient missing in the midfielder's search for contentment.
"I am writing this (blog) from the hotel room where I have lived since I arrived in Manchester a week ago," said the Spain international, who was pictured house-hunting in Cheshire last week.
"For the next post I hope I can write from my own house; I'm looking forward to find it!"