The Ivorian forward has completed a £12million move from Vitesse to the Liberty Stadium, making him the Swans' record signing.
He made his debut for the club in a friendly at Den Haag last weekend, but is yet to be cleared to make his way to South Wales.
Swansea boss Michael Laudrup is confident the issue will be resolved shortly, allowing Bony to become a permanent part of his plans.
He said in the South Wales Evening Post: "The club are still working on Wilfried's work permit.
"He's still in Holland and we gave him permission to train with Vitesse because otherwise it would be too many days without doing anything.
"It's something we have to cope with as he is a player from outside the European Union.
"He hasn't been to Swansea yet, but I hope he will be here next week. I heard from the club and they hope it will be during this week. It would be nice to have him back for training on Thursday.
"It's best to have the player here. Now we've signed him it's not so good if he is only in Holland. We want him here."