Reports suggest that the Tigers are prepared to part ways with the Croatian striker who has been made available for a cut-price £3million.
It is believed that Italian club Napoli, Turkish side Trabzonspor and UAE outfit Al Ahli are all showing interest in Jelavic.
The 29-year old arrived at Hull from Everton for £7m in January 2014 but is not keen to drop down to the Championship with the Humberside club.
"Jela does not fancy dropping down a division at this stage of his career, and Hull have told him they won't stand in his way if the right move comes along for him," a source told the Daily Mirror.
"In any case, the club know they have got to streamline the wage bill after losing their top flight status, so that's another reason why they're prepared to cut their losses on Jela."