The Mirror says Delaney's future is a pressing matter as the Ireland defender's current contact expires next summer.
And after winning over new Eagles boss Neil Warnock, Delaney, 33, will be rewarded with an extension. But the south Londoners have also moved to keep Ward long-term.
The versatile defender has attracted interest from Liverpool, prompting Palace chief Steve Parish to move.
Parish said: "We obviously want to keep our best players here."
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