The Brazilian was keen to make the move on a full-time basis, but the club reportedly opted for a €6.5 million set fee in the summer if the switch is a success
The Brazilian, who has made just four Premier League appearances this season, is currently in Florence ahead of a medical, with the deal set to be announced on Thursday.
According to reports in the Italian media, Anderson was keen on joining Fiorentina on a full-time basis but United vetoed the proposal in favour of a set €6.5 million [£5.4m] fee in the summer.
The loan frees up space for Moyes to delve into the transfer market during January, with the Scot recently spotted at the Sant'Elia Stadium casting an eye on Juventus midfielder Claudio Marchisio.
Goal understands Moyes has been given €180 million to spend in January and over the summer, and will overhaul his squad by allowing a number of players to leave Old Trafford, with Anderson expected to be the first.
Anderson arrived at Old Trafford from Porto in a big-money move in 2007 with the reputation of an attacking midfielder, but has scored only nine goals in 179 appearances.