Swans boss Michael Laudrup is desperate to sign a new striker and after watching a number of targets slip away in recent weeks, he is hoping for more luck with Gomis.
First of all chairman Huw Jenkins has to sanction such a big outlay that would smash the club's transfer record, and failure to do so would frustrate Laudrup even more.
The Dane is unhappy that he has only been able to bring in Jose Canas this summer and that has caused friction between himself and Jenkins.
A swoop for Gomis would bring a smile to his face, but he also faces competition from arch rivals Cardiff City, who are looking to strengthen after winning promotion to the Premier League.
Arsenal have previously been linked with Gomis but they are pursuing other targets and will leave Swansea and Cardiff to scrap it out for his signature.