Reports on Friday linked Liverpool with a move for the Ivorian forward as they look to replace Luis Suarez, who, it was announced on the same day, is moving to Barcelona.
The Anfield outfit were even said to be in talks with Bony's representatives but Jenkins scotched those rumours, stating that the two clubs had not even spoken about the player.
And Jenkins is confident Liverpool have not broken transfer rules, which state that clubs cannot approach contracted players before an agreement is reached.
"I have had no talks with Liverpool until now," Jenkins told the South Wales Evening Post.
"I would be very surprised if a club like Liverpool are doing any kind of negotiations with a player or player's agent behind our back.
"I would have thought somebody from Liverpool would have been in touch if they are really interested in Wilfried.
"There's a way of doing things. I know things are different in this day and age, but the usual rule of thumb is that when you are trying to complete a transfer, you deal with a club first and then the player comes after that. That's the nature of the system."
Bony is reported to have a £19 million buy-out clause in his contract. The 25-year-old joined Swansea from Vitesse for £12 million just over one year ago.
And he proved an instant success, scoring 26 goals in 48 appearances last term.
Thank you for reading 5 articles this month* Join now for unlimited access
Enjoy your first month for just £1 / $1 / €1
*Read 5 free articles per month without a subscription
Join now for unlimited access
Try first month for just £1 / $1 / €1
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.