The 32-year-old scrum half has been skipper for the past three seasons -seven in all.
He said: "I have done my stint and I think it is time to hand the reins over to someone else. I have been involved with the club for a long time and the idea next season is to help out with the coaching."
Jenkinson, however, says he is not quitting playing, despite a long-term knee injury which almost ended his career earlier this season.
He also suffered a shoulder injury which responded with rest.
"I'm keen to keep playing, if selected, of course," he added. "I will see how pre-season goes."
Looking forward to next season, Jenkinson added: We certainly need to improve our away form if we are going to be considered serious title contenders.
"Were looking to put a plan in place for next season and to start training earlier this summer - in the middle of June. If we have thoughts of promotion, we need to get off to a good start - and that means a good pre-season."
Greg Dyke, the club's president said: "We really appreciate everything Tim has done for the club. He has led by example and we hope he will continue playing as long as he can."