Il Corriere dello Sport says PSG are preparing a €60m bid for Kone.
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A move next summer is planned for the youngster, though a January push hasn't been ruled out.
Kone joined Roma last year on-loan from Borussia Monchengladbach before signing permanently over the summer.
Roma paid €18m to buy Kone outright and now stand to make an impressive profit should they agree to terms with PSG.