Kelly moved to Juve on-loan in January from Newcastle before being signed permanently at the end of the season.
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However, Juve are prepared to sell on the defender for a quick profit.
And Il Corriere dello Sport says Palace are in contact with Juve about a deal for Kelly this coming week.
Palace see Kelly as a replacement for Marc Guehi, who is expected to be sold to Liverpool after the second-leg of their Europa Conference League playoff second-leg at Fredrikstad on Thursday.