The 21-year-old Kalinic currently plays for Hajduk Split and reports on Tuesday suggested he is on the verge of a £5.5million transfer, although Hart refused to speculate on that.
"Steve Finnan is one of many people we are interested in. As is Nikola Kalinic," said Hart.
"Steve is a quality player and if you saw my list you could probably see a few more quality players there.
"He's a very experienced player, like many others on the list."