The 29-year-old joined the London club from Bayer Leverkusen for £16m last summer but has since struggled to find the net. In 17 league appearances, the forward has only managed four goals with the last coming in a 2-2 draw with Crystal Palace on 28th October.
Current manager David Moyes, who took over West Ham at the beginning of November after the dismissal of Slaven Bilic, has already lifted the 'Claret and Blues' out of the drop zone and is looking to push on by bringing in some reinforcements in this transfer window.
In a squad shake-up, which could also see Diafra Sakho, Andre Ayew and Andy Carroll out the door for the right price, the former Manchester United manager wants to reshape the Hammers' attack with 'Sky Sports' also alleging that Krasnodar striker and Russian captain Fyodor Smolov could be on his way to the east London side.