The Cote d'Ivoire international is keen to move to the Premier League outfit even though Vitesse had earlier denied reports a €12 million 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 are willing to match Vitesse's asking price of €12 million.
"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 €12m 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."