The Swans are understood to be close to agreeing terms with the player, but despite lengthy negotiations are seemingly unable to come to agreement with Vitesse.
Jenkins has now admitted that the Premier League club may have to consider going for their 'plan B'.
"It's very difficult and gradually we are becoming frustrated," Jenkins told De Telegraaf.
"If it does not work with Bony we need to go for our plan B."
Bony, for his part, somewhat reluctantly returned to pre-season training with Vitesse on Wednesday, and he would not comment on his future.
"At the moment it is unwise to say anything," said Bony.
Meanwhile, Jenkins also revealed that the club had backed away from FC Twente forward Nacer Chadli because the player was not ready to commit.
"The player wants to wait, so we shifted the interest to others," said Jenkins.
Bony, 24, has already confirmed he would be more than happy to move to South Wales, and Michael Laudrup would be pleased to have him or even Chadli.
"Actually I should not talk about players who are not here," said Laudrup in De Telegraaf.
"But everyone knows that we are looking at forwards across Europe, and those two [Chadli and Bony] have done very well in the league. They are both interesting players."