Kalinic is no stranger to English football, having previously spent two years with Blackburn Rovers, where he scored 13 goals in 53 games.
But after an impressive spell with Ukrainian side Dnipro, the 27-year-old Croatian is back in the limelight with Fiorentina.
Kalinic only signed with La Viola last summer but has wasted little time in impressing in Italy with 10 goals in his first 13 games for the Serie A side.
That has been enough to pique the interest of Chelsea manager Jose Mourinho who is on the lookout for goalscoring reinforcements at Stamford Bridge and is taking a close look at the ex-Rovers man, according to Gazzetta Dello Sport.
Diego Costa has endured a difficult season with the Blues thus far while Radamel Falcao has yet to impress since moving to the West London club on a season-long loan.
While no transfer fee has yet been mentioned, a return to the Premier League would represent a remarkable reversal of fortunes for Kalinic, who was once deemed surplus to requirements at Ewood Park by Steve Kean.