Gomis has reportedly said he is unhappy with the role he has been playing at the Liberty Stadium.
Gomis reportedly claimed to French TV that he hadn't been given the game time promised by the Swans when he signed a new deal at the Liberty Stadium in the summer.
Following the big-money sale of Wilfried Bony to Manchester City, manager Garry Monk will not want to lose another striker, having brought in Nelson Oliveira on loan from Benfica.
Crystal Palace are rumoured to be interested in the striker, and it has been reported that Swansea are likely to receive an £8 million fee for the forward who only linked up with the South Wales club in the summer.
Given the loss of Bony, it's unsurprising that Garry Monk would want to keep hold of his striking options, but if Gomis were to depart it would be hard not to see them trying to enter the transfer market to bring in some kind of replacement.
If Gomis were to stay, it's hard not to think that he will feature on a more regular basis going forward, and the report shows is an indication of Swansea's desire to keep hold of the Frenchman. Another indication will be that he started the weekend's defeat to Chelsea at the Liberty Stadium as they began life after Bony.
The risk the club would run, of course, is keeping an unhappy player at the Liberty Stadium, and potentially causing unrest after what has been a promising season for the side so far.