The Ivorian had been linked with a £20 million switch to Anfield, with Brendan Rodgers assessing possible replacements for Luis Suarez, who has now been confirmed as a Barcelona player.
However, Swansea City chairman Jenkins says the Reds have had 'no contact' with him over signing Bony, suggesting that the likelihood of Liverpool speaking to the striker behind the club's back would be very low.
"I have had no talks with Liverpool until now, and 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," Jenkins told the South Wales Evening Post.
"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."
Similar quotes have been attributed to the Swans chairman by the Daily Mail, while Goal.com are reporting that Rodgers' side are now considering Loic Remy as an alternative option. The Evening Standard also say that Tottenham have now rivaled the Reds' bid for Bony.
Liverpool's list of strikers already at Anfield includes Daniel Sturridge, Rickie Lambert and Fabio Borini.