Transfer-listed ahead of the January market by Chelsea, Disasi has attracted interest from AC Milan and Olympique Lyon.
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.