The club announced it will announce managerial plans within 24 hours.
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“I have had an excellent working relationship with Paul and we are all, including the owners, surprised and disappointed it hasn’t worked out this season,” Jenkins wrote on Swansea’s site.
Clement was hired on a 2.5 year deal in January after Swans fired Bob Bradley, who himself replaced fired Francesco Guidolin. Both Guidolin and Clement led the team to Premier League safety, only to be fired the next season.
Swansea sits dead last in the Premier League through 18 matches, four points back of safety. It next hosts Crystal Palace.
Clement finished 14W-5D-22L.