The British tabloid reports that West Ham made an offer of £8.4 million for the 29-year-old striker, but the Swans have turned it down.
It has been claimed that the Hammers made the move in case Chelsea make a late approach for forward Enner Valencia, who has been one of the best players for them.
Swansea chairman Huw Jenkins has also made it clear that Gomis is not for sale on transfer deadline day.
“There is no chance of Gomis going anywhere," he told The South Wales Evening Post. "There are not many strikers out there so someone like him will always stand out in the market, but we are not going to sell."
Good decision from Swansea City?
Gomis has not been in exactly great form so far this season following his move to Swansea in the summer of 2014 on a free transfer after leaving French giants Lyon.
The France international has scored just one goal and created only 10 chances in 19 Premier League appearances, while having a pass accuracy of 82% and a shot accuracy of 21%.
However, with Wilfried Bony gone to Manchester City, Gomis is now likely to play a major role for Swansea for the rest of the season.
The Welsh outfit simply cannot afford to lose the Frenchman at this stage of the January transfer window as signing a replacement for him would be a huge problem.