Right-back Clyne, 29, was released by the Premier League champions back in June having missed all of last season because of a cruciate ligament injury.
Clyne came through the academy ranks at Palace and played 137 times for the club between 2008 and 2012 before signing for Southampton.
Palace boss Roy Hodgson said: "He didn't train with us today, I haven't seen him.
"He was coming to be tested so he could take part in some training over the next couple of weeks where he is keen to show his fitness to us and other clubs.
"We are happy to welcome him into the fold and give him that opportunity."
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