The Croatia international is currently plying his trade with Fiorentina in Serie A, where he has impressed with nine goals in 12 appearances.
This form has, according to reports, attracted the interest of Chelsea, who are currently short of firepower.
Star forward Diego Costa has notched only three Premier League efforts this term and has looked off the pace, while back-ups Loic Remy and Radamel Falcao have been overlooked by Jose Mourinho on many occasions.
Kalinic was a Blackburn player between 2009 and 2011, but struggled to make an impact in a misfiring Rovers side before moving on to play for Ukrainian giants Dnipro Dnipropetrovsk – whom he featured in the Europa League Final with last season.
A move for the 27-year-old may tempt Mourinho, as the striker remains eligible to play in the Champions League – Chelsea must avoid defeat in their last game against Porto to reach the last 16.