The report claims the Italian club will increase his salary from around £9,500-a-week to £12,000-a-week.
The new deal, which is designed to keep the Colombian international from the clutches of Arsenal and Barcelona, will not extend his current deal past its current expiration date of summer 2017.
Cuadrado spent last season on loan in Florence before making his move permanent over the summer, and he's impressed again this term.
He's scored four in all competitions, leading to speculation that Fiorentina had already slapped a £20m valuation on him to warn off interest from the likes of Arsenal and Barcelona.
But they're not the only clubs keen on the 25-year-old. Bayern Munich are also thought to be monitoring his displays in Serie A with a view to a potential bid in the January transfer window.
The versatile Colombian - he can also play in defence as well as midfield - has two goals and two assists in seven appearances for sixth-placed Fiorentina in the league this season.
Arsenal are thought to be already planning for the January market, as they look to build momentum through the New Year following the Gunners strong start in the Premier League campaign.