The Brazilian joined the Italian club last month on a deal until the end of the season.
However, the 25-year-old has now suggested that he wants to stay beyond the summer.
"I have to play and have my chance," he told The Sun. "It is better for me at Fiorentina. The manager wants me and has shown his trust. I can show him my football.
"Even though the contract is only on loan, I want to stay for a long time."
Anderson made his first appearance for Fiorentina last Saturday during a 1-0 defeat at Cagliari in Serie A.