The Manchester United midfielder travelled to Italy on Thursday for talks with the Serie A club's sporting director Daniele Prade.
Fiorentina posted a photograph of the talks on their website and said a medical would take place today.
And United boss David Moyes later confirmed a loan deal rather than a permanent transfer was the plan.
He said: "We've not been able to get him as many games as we hoped. We feel it's a good opportunity for him - he's going to a good club in a good league so hopefully that gets him some benefit."
Anderson has struggled for first-team football under Moyes in in seventh season at Old Trafford.
The Brazil international, who cost a reported £27m when he joined United from Porto in 2007, has made just four Premier League appearances since Sir Alex Ferguson's departure.