Jelavic fled Bosnia and Herzegovina last year after being convicted for embezzlement.
Sarajevo's Dnevni Avaz daily quoted Kirin on Monday as saying that as a member of Interpol Croatia would honour its international commitments in Jelavic's case and arrest him, provided that it obtained an Interpol warrant and that the former Bosnian Croat official was in Croatia.
"Our police have not received either an international warrant or any other document from the Bosnian authorities in connection with Jelavic," said Kirin.
The director of Interpol Bosnia and Herzegovina, Brane Pecanac, said a warrant to locate and arrest Jelavic, "with special emphasis on our colleagues from Croatia", was issued immediately after he fled the country.
Commenting on the issue of extradition, Kirin said it was an entirely different matter because Croatian law prevents the extradition of Croatian citizens, unless there exists an interstate agreement regulating this issue differently.
Kirin went on to say that the Croatian police did not have information that Jelavic was in Croatia, despite media allegations based, among other things, on the fact that Jelavic owns real estate in Split and his wife in Zagreb.
The minister said there were no records of Jelavic having crossed the Croatia-Bosnia border but conceded that illegal border crossings between the two countries were at least twice the number of official ones.
Last year Bosnia's State Court sentenced Jelavic to 10 years in jail, with the right to appeal, for redirecting, via the Mostar-based Hercegovacka Banka, money which Croatia had been sending as assistance to Croats in Bosnia.