The Swans have offered their captain new terms to take him beyond the automatic one year extension that he triggered with his appearances last season. Monk was outstanding at the heart of defence as his side won promotion to the Championship and he was voted players player of the year as well as being nominated in the PFA League One team of the season.
"We have offered Garry improved terms and we are waiting to hear from him," the Swans chairman told the Evening Post. "We fully expect him to take up the offer.
"We feel that Garry was a major part of our achievement in winning League One, and when you take into account the great season he has had as captain he deserves this deal."
Monk has always expressed his desire to stay at Swansea and there seems nothing to suggest that he won't sign that deal as soon as possible.
Jenkins also hinted at possible future arrivals to the Liberty at the back and added "It was our priority to get another defender in and I would assume that maybe more will come in."