The 25-year-old left Old Trafford during last month's transfer window to link up with Fiorentina on a loan deal.
"I'm sure that lots of players want out, especially players like myself and Nani who have been in Manchester for seven or eight years," the Manchester Evening News quotes Anderson as saying.
"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."
The former Porto player went on to admit that he has no intention of making a return to United once his loan deal with the Viola has expired in the summer.
"I am grateful to be here to try and win as many titles as I have in Manchester. Definitely I want to stay here," he said.
"Playing in Manchester was great, it's a prestigious club with a lot of history but I've been there seven or eight years and I'm grateful to be here to show Fiorentina what I can do and fight for a spot in the starting lineup.
"I'd like to thanks Manchester United fans for their love, but I'm here to stay."
Anderson has made two appearances in Serie A so far.