Kalinic, 25, has come up through the ranks with Hajduk having joined the club at the age of ten, and after a series of loan moves away, he is certainly their first-choice goalkeeper now.
With two caps for Croatia, Kalinic is starting to make a name for himself, and it seems that his exploits with Hajduk are attracting interest.
Reports from the Daily Mirror over the weekend suggested that Aston Villa are very keen to sign Kalinic in a deal worth nearly £3m in January, with goalkeeping scout Tony Coton impressed with what he has seen from the giant shot stopper.
Standing at 6ft 7in tall, Kalinic is an imposing figure between the sticks, but Villa seemingly aren't the only Premier League club interested in signing him.
The Daily Mail report that Leicester City and Sunderland have both joined the race to sign Kalinic, and are hoping to beat Aston Villa to his signature next month.
Leicester have long-term custodian Kasper Schmeichel between the sticks, but 43-year-old backup Mark Schwarzer won't have too much longer left in him, and manager Claudio Ranieri could target Kalinic as an option to push Schmeichel.
Meanwhile, Sunderland boss Sam Allardyce seemingly can't decide between Costel Pantilimon and Vito Mannone as his first-choice goalkeeper, but that situation could be rectified with the seemingly imminent return of Jordan Pickford from his loan spell at Preston North End.
If Pickford does return to the Stadium of Light, it's hard to see Allardyce targeting another goalkeeper - which would be good news for Villa and Leicester.