The Swans are actually already in Holland on a pre-season training camp, and during their stay across the Channel they have been locked in talks with Vitesse Arnhem.
Bony's agent last week hit out at Vitesse's failure to agree terms, but now the club record move is close to completion with the deal worth around £13.7million (€16million).
"Until it is signed we cannot speak about an agreement, but there are only a few details now," Jenkins is quoted by De Telegraaf.
"We want it done by lunchtime [on Monday] or so. We have the last few details to sort with his representative, but that won't be a problem.
"He will have his medical in Holland before joining up with the team."