The Blues lack of success in front of goal this season has lead to the club heading to the transfer market in search of new options.
The strikers form could well fill that gap Chelsea are looking to fill, he has 10 goals in his nine Serie A appearances so far this season.
Kalinic will be slightly familiar with the English game after already spending time over here with Blackburn Rovers in the past.
The Croatian would also be eligible to play for Chelsea in the Champions League this season if the deal goes ahead.