Remy is on-loan from QPR and has been linked with Arsenal.
Pardew said: "Like all strikers, he wants to achieve the best he can for himself. I suspect that will be international football and Champions League.
"One of those we can cross, which is international football because he has been in the France squad and he will have a good chance of making the World Cup.
"Champions League football is the next one. In the summer that is the bridge that we have to persuade players we can cross.
"I know he loves it here and enjoys working with my staff and it is all about flourishing when you get an opportunity.
"I don't think he flourished half as much at QPR as he has here."
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