Ivica Olic looks to be on his way back to Hamburg, with Andre Schurrle increasingly likely to join Wolfsburg.
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 €12million (£10.2million) for the highly-rated forward and his signing would be something of a coup for Laudrup.
Bony has since revealed that he is keen on sealing the move.
"The clubs are now talking to each other, Swansea has made Vitesse a bid and I hope it's good," Bony told Voetbal International.
"Swansea is a wonderful club. It's my chance to play in the Premier League and they also play attractive football.
"I understood from my agent that Swansea want to pay €12million for me and that is what Vitesse want to receive, so I hope there is some good news soon."
Vitesse Arnhem have denied reports the striker is set to make an imminent move to Barclays Premier League.
The club posted a statement on their website which read: "Various media have reported that Wilfried Bony is to transfer to Premier League club Swansea City. This message is incorrect.
"There is admittedly much interest in the striker, the top scorer in the Eredivisie last season, and Swansea City are one of the interested clubs. However, a transfer is not the case."
Swansea are also closing in on the signing of £2million rated Espanyol defender Jordi Amat, while Real Betis midfielder Alejandro Pozuelo is set to join his former team-mate Jose Canas in south Wales.
Swansea are also in talks to bring Jonathan de Guzman back to the Liberty Stadium on a second season-long loan, while bids have been lodged for Birmingham winger Nathan Redmond, Lyon striker Bafetimbi Gomis and Standard Liege forward Michy Batshuayi.