Bony has been linked with a host of English clubs following his goalscoring exploits for Vitesse over the last couple of seasons.
The likes of Newcastle, Sunderland and Arsenal have been linked with moves for the Ivory Coast international, but Swansea are hoping to win the race for Bony's signature.
Swansea boss Michael Laudrup has made a new striker one of his top priorities this summer as he looks to ease the goalscoring burden on last season's top scorer Michu.
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 €12million (£10.2million) for the highly-rated forward and his signing would be something of a coup for Laudrup.