The England international's future is expected to lie away from Selhurst Park in 2026.
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Wharton has been linked with Manchester United and Liverpool over the past 12 months.
However, AS says agents for the player have made contact with Real Madrid in an attempt to open initial negotiations.
For the moment, the feedback has been Real won't be seeking to do business in January for Wharton, though talks could be held closer to the end of the season regarding a summer deal.