The Ivorian striker has previously stated his desire to make the move to the Liberty Stadium but the Swans have grown frustrated with the lack of progress in talks
The Ivory Coast international, who scored 37 times in 36 appearances for the Eredivisie outfit last season, has been one of the Swans' top summer transfer targets as Michael Laudrup looks to add more firepower to his squad ahead of their maiden voyage into Europe next season.
|20/1||Swansea are 20/1 with Bet365 to finish in the top four next season
"It's going to be very difficult and we have gradually become frustrated," he told reporters.
"In the not too distant future we want clarity. If it doesn't work out with Bony, we have to move to plan B."
Negotiations with Bony were previously said by Swans director John van Zweden to be "pretty far apart", while Lyon have also revealed the South Wales club have made an offer for Bafetimbi Gomis.
Jenkins revealed the Swans have also experienced frustration over another prospective transfer target, Belgium international winger Nacer Chadli.
"The player wants to wait, that is why we have the interest has shifted to others," he confirmed.
Liverpool midfielder Jonjo Shelvey became Swansea's fifth summer signing on Thursday.