Bony has been heavily linked with a move away from the Liberty Stadium following an impressive debut season in South Wales, with Liverpool and Tottenham thought to be interested in his services.
After signing from Vitesse, Ivory Coast international Bony scored 26 goals in all competitions for Swansea last term before going on to the find the net twice in three games for his country at the World Cup.
Liverpool's move for QPR striker Loic Remy fell through last week after the France international reportedly failed a medical, reigniting talk of a potential approach for Bony from the Anfield club.
Swansea manager Garry Monk indicated only an "astronomical fee" would see them part ways with Bony, but Jenkins accepts that it would be difficult to deny the 25-year-old a switch if a UEFA Champions League club were to make a bid.
"Wilfried Bony is a fantastic professional," Jenkins told talkSPORT. "If a top Champions League club comes in, and puts the right offer on the table, then of course we will speak to him.
"There are no issues with Bony. He's a great guy to have around the club.
"As much as we want players to stay with us for a number of years, we have to be open."
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.