The Poland international is only tied to the Stadio Franchi side until June 2022 and negotiations for an extension have hit problems, as he is requesting €2m per season wages.
He could be the perfect replacement for his fellow countryman Fabianski who entered the final year of his contract with West Ham.
According to Sportitalia, Tuttomercatoweb and TVP Sport, Dragowski will be available at the right price with Serie A club Atalanta leading the way with others including West Ham interested.
Fiorentina wants €30m for their goalkeeper, while his true valuation is probaalby closer to €15m.
The Poland international has been in impressive form since joining the Serie A outfit in the summer of 2016, with 79 league appearances under his belt.