Terry announced on Sunday that his expiring contract will not be extended by the Blues only for the club to later insist that they will "keep the channels of dialogue open" as they search for a permanent manager.
The 35-year-old ruled out the possibility of joining another Premier League club if he does leave Stamford Bridge but that will not discourage Pardew from making an approach.
"I've bumped into John Terry on occasion and asked him many times to join me," the Palace boss told reporters. "He always sniggers at the suggestion.
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"Of course I will ask one more time. I'm sure I'll bump into him again and ask the question."
Pardew added: "He's got a winning mentality that anyone would want. I've seen his comments about leaving Chelsea and he's probably called it right.
"He'll have plenty of options – MLS, Gary Neville has gone to Spain, and there's China. He's got now until the summer to decide the right move for him and his>