Benteke, 30, sees his contract at Selhurst Park expire on June 30.
But with Belgium's tournament getting underway 18 days earlier, Benteke may sort out his future beforehand.
But they are worried they will face competition for his signature, especially if he performs well at the rearranged tournament.
The report adds interim boss Emre Belozoglu wants a deal with Benteke over the line 'as soon as possible'.
He may even resort to negotiating directly with the 39-cap Belgium international if talks with his agent are slow.
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