Bony's agent, Francis Kacou, has claimed the 24-year-old is on the verge of a move to the Liberty Stadium, with only minor details to be sorted.
"Bony will go to Swansea," Kacou told Dutch newspaper de Gelderlander.
"For how many years? We still have to work out that part. Hopefully more will be clear today."
Swansea are believed to have agreed a fee in the region of £10.2million.