Gomis only moved to Swansea in the summer, but he has become frustrated with his time there so far as he had to play second fiddle to Wilfried Bony.
Even though Bony has now left the club, and he has been assured of his place in the first-team, he is still hoping to depart the Liberty Stadium and West Ham apparently looks an appealing move.
Impact for Swansea?
The loss of Gomis would be a huge blow for the side. Before Bony left, the Welsh outfit could have sacrificed the Frenchman, but his departure would now leave a big void in the side.
Swansea have very few options up-front and Garry Monk would face a tough test ensuring that his side still posed any sort of goal threat if Gomis did leave.
The Frenchman may have not been in red-hot form since moving to England, but his power and pace still makes him a dangerous opponent and Swansea would struggle to find a replacement of similar quality with so little time remaining in the window.