The 24-year-old, who ended as the Eredivisie's top scorer with 31 goals last season, claims the Premier League club are willing to meet his side's £10.2m asking price
The Ivory Coast international, who has also been linked with a switch to Newcastle United, has claimed Michael Laudrup's side are willing to match Vitesse's asking price of £10.2 million.
|33/1||Swansea are 33/1 with William Hill to finish in the top four
"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 €12 million [£10.2m] for me and that is what Vitesse want to receive, so I hope there is some good news soon."
Bony helped guide Vitesse to a fourth-placed finish last season and finished as the Eredivisie's top scorer with 31 goals.
Earlier on Thursday, Vitesse denied reports claiming a deal had been agreed with Swansea for the 24-year-old.
"On Thursday afternoon June 27 appeared in various media reported that Wilfried Bony to move to Premier League club Swansea City. This message is incorrect," read a statement from the Eredivisie club.
"For the striker, top scorer in the Eredivisie last season, there is admittedly much interest and Swansea City are one of the interested clubs. However, a transfer is not the case."