The Welsh club's chairman claimed the club are close to what would be a club-record fee for the Ivory Coast international striker, who scored 31 goals in the Eredivisie last season
The 24-year-old finished as Eredivisie's top goalscorer last season with a remarkable return of 31 goals in 30 games, collecting the Dutch Footballer of the Year award as Vitesse finished fourth.
| TRANSFER TALK
|66/1||Michu is 66/1 with BetVictor to finish as the Premier League's top goalscorer
"As long there's not signed, there's no agreement", Huw Jenkins told De Telegraaf.
"But it's now up to a few details. We want this finished around [Monday] lunchtime. We're talking about the final deals with his manager, but that won't be a problem.
"He could get his medical in the Netherlands and join the team after that."
Swansea have also had a bid accepted by Lyon for striker Bafetimbi Gomis, but Jenkins insists the club will only sign one striker this summer.
"Realistically, it has to be one or the other," Jenkins told the South Wales Evening Post.
"We had a bid accepted for the player [Gomis] but, if we sign Bony, it is unlikely we will sign both."
Michael Laudrup has been busy already this summer, having already signed Jordi Amat, Jose Canas, Jonjo Shelvey and Alejandro Pozuelo as well as extending Jonathan de Guzman's loan deal for another season.