The 25-year-old France international is expected to be available for transfer despite being under contract until 2029.
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Roma's financial situation is likely to force the club into player sales, with Kone among those attracting significant interest.
Arsenal have been linked with the former Toulouse midfielder, but Atletico Madrid are also pushing strongly for his signature.
According to L’Equipe, Atletico representatives have made several scouting trips to watch Kone in action and have identified him as their top midfield target.
Should a move for Koné fail to materialise, the LaLiga team are reportedly considering Parma's Belgian midfielder Mandela Keita as an alternative option.