Transfer-listed ahead of the January market by Chelsea, Disasi has attracted interest from AC Milan and Olympique Lyon.
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TMW says Roma chief Ricky Massara has made an approach to Chelsea in the last 48 hours for the centre-half.
While Massara is seeking a new striker signing, he is also eager to add a low-cost centre-back to coach Gian Piero Gasperini's squad next month.
Disasi has emerged as a prime option, though Massara will have to battle Serie A rivals Milan to land the Frenchman if he is to move to Italy in January.