Gian Piero Gasperini regards the France international as untouchable, and with roughly ten days of the window remaining, the club's sporting management have made clear that only an offer above €55m would even open the door to a sale.
Alongside Atletico Madrid, that has not stopped English interest circling. Manchester United remain watchful despite having already signed Andrey Santos and moved close to completing a deal for Brighton's Carlos Baleba, while Manchester City have also emerged as suitors under Enzo Maresca, who is searching for further central-midfield reinforcement following the departures of Rodri and Tijjani Reijnders and the arrival of Elliot Anderson from Nottingham Forest.
City are weighing Koné alongside Chelsea's Enzo Fernández and Lille's Ayyoub Bouaddi, though both carry higher price tags.
AS Roma's position remains firm regardless of the interest: none of the squad's key pieces are for sale without a substantial offer, and without a major financial step-up from any of the interested English clubs, Koné staying in the Italian capital for the season just begun remains by far the most likely outcome.
The club have been more active on incomings. Roma have submitted an offer to Fenerbahçe for Jayden Oosterwolde on the basis of a loan with an option to buy, a package that including add-ons is worth close to €20m in total, according to Turkish journalist Yağız Sabuncuoğlu.
The 25-year-old Dutch defender, who can play at left-back or centre-back, previously spent a season in Serie B with Parma before joining Fenerbahçe in 2023, and has become a regular starter in Turkey over the past three seasons.
Before pushing ahead with the move, Roma carried out a thorough assessment of his fitness following a recent injury; those checks found he should be ready to return to action within three weeks, meaning the club expect to have him available before long once the transfer is completed.