The 22-year-old former Milan striker had only joined Wolverhampton Wanderers in the summer for €18m plus bonuses.
According to multiple Italian sources, this will be an 18-month loan at a cost of €3m with option to buy for a further €18m, which will become an obligation if certain conditions are met.
Wolves would then have a buy-back option, but Fiorentina have the final word with another counter-option they can activate within five days for a higher fee.
Cutrone scored three goals in 24 competitive games for Wolverhampton Wanderers.