The Cote d'Ivoire international is keen to move to the Premier League outfit even though Vitesse had earlier denied reports a 12 million euro deal was in the offing.
The Ivory Coast international, who has also been linked with a switch to Newcastle United, has claimed Michael Laudrup's side is willing to match Vitesse's asking price of 12 million euros.
"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 12 million euros 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."