Following Hull's relegation to the Championship, Jelavic has been one of the many high profile names touted to leave the KC Stadium this summer.
Despite interest from Turkish club Trabzonspor as well as the Middle East, Hull still have not received a firm offer for Jelavic and Bruce has stated that he would be happy to hang onto the Croatian international for next season.
Bruce told the Hull Daily Mail: "It's gone quiet on Jela, thankfully. Let's hope that continues all summer. He's contracted to us and if nobody wants to buy him then, of course, he will stay with us. If that's the case then fine. A fit Jelavic would be a real handful in the Championship."