Gomis, who only joined Swansea City this summer, has become frustrated with his limited first-team opportunities at the Liberty Stadium and he is already hoping for a move away.
The powerful striker has found himself behind Wilfried Bony in the pecking order at the Welsh club and he has had to make do with substitute appearances throughout his time at Swansea so far.
With Bony heading off to the African Cup of Nations, it was expected that Gomis would have a crucial role to play for the Swans during the coming month, but it seems that he is intent on leaving.
The 29-year-old is available for around £7 million and there are a host of Premier League clubs chasing his signature.
Newcastle United and Crystal Palace have been long-term admirers of Gomis, but West Ham's and Villa's rising interests mean that he should have no shortage of options should he opt to move on.
Gomis has scored four times for Swansea so far in all competitions and he has clearly shown enough to prove that to other teams that he is ready to perform a function in England.