Clement worked with Terry during his time as an assistant coach under then Chelsea manager Carlo Ancelotti in the 2009-10 season.
With Terry announcing he will end his long association with Chelsea at the end of the season in a bid to find regular first-team action, Clement admitted on Thursday he would love to bring the 36-year-old to south Wales.
But Clement accepts the only chance Swansea have of signing Terry is if they climb out of the relegation zone.
“If we stay up why wouldn’t we be interested?” asked Clement, whose team are two points from safety with five games left.
“I know John very well as a player and a person and I would be more than happy to speak to him.
“When the season finishes we can have those discussions about our own players and potential targets.
“But having worked with John, I know what a fantastic player he is and what a career he has had.
“He has unbelievable talent and he is a fantastic leader — one of a dying breed of leaders.
“He has represented that club so well over so many years in a time when players are too quick to move on and go from club to club.”
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