The Brazilian has told friends he wanted a permanent move to ensure more playing time but that United only wanted to sanction a loan move at this time.
Anderson left Frankfurt on Thursday Morning – having connected from Manchester – and the loan should be in place by lunchtime on Friday.
Anderson has made just four appearances for United in the Premier League this season, and eight overall.
He joined United in 2007 from Porto for around £20million, making 179 appearances and scoring nine goals since.
Meanwhile, Fiorentina have injuries to Giuseppe Rossi and Mario Gomez which means they are rivalling Premier League sides for the trio of strikers being offered around on loan from Italy; Roma’s Marco Borriello and Juventus pair Mirko Vucinic and Fabio Quagliarella.