Jelavic joined West Ham from Championship side Hull City in the summer of 2015.
The British newspaper has reported that West Ham will sell Jelavic in order to raise funds for two of their January transfer targets - Leeds United defender Sam Byram and Juventus striker Simone Zaza.
Byram, who can play as a right-back or as a right-winger, has been at Leeds his entire career, but his current contract with the Championship club runs out at the end of the 2015-16 campaign.
Zaza moved to Juventus from Sassuolo in the summer of 2015, but he has scored just three goals and created three chances in nine Serie A games so far this season.
The London Evening Standard claims that Chinese Super League club Guangzhou Evergrande are favourites to sign Jelavic from West Ham in the January transfer window.