The defender made his first return to Selhurst Park on Saturday as Southampton recorded a 1-0 win, but Clyne was suitably impressed with Palace's display.
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"I would love to see my old club stay up," he told the Croydon Advertiser. "It is nice to see them playing in the Premier League where the fans deserve it.
"I think they've got a great chance in staying up, especially with them at home.
"They're getting points at home and they will be vital for them.
"If they get the wins at home, they can definitely stay up."
After four years at Palace, Clyne moved to Southampton in 2012 and has made 60 appearances for the south-coast club in all competitions.