Koné has emerged as one of the most in-demand midfielders in Europe following an excellent season at Roma, where his form has helped establish him as a regular for France, with whom he reached the World Cup semi-finals this summer under Didier Deschamps.
AS Roma fought off considerable competition to keep hold of him over the summer, a priority for a club aiming to compete for silverware and back in the Champions League this season.
According to journalist Simon Phillips, Chelsea are now planning to move for the 25-year-old in January having already tried and failed to sign him during the summer window.
Roma themselves confirmed Chelsea's earlier interest but said no formal offer was ever submitted. Phillips also reports that Jamie Gittens, a player who has struggled for game time under Xabi Alonso this season and has recently attracted interest from Roma, could be included as part of any structured deal between the two clubs.
Chelsea's need for a new midfielder has become increasingly pressing since deadline day, when the club sold Enzo Fernández and failed to complete a deal for Monaco's Lamine Camara despite believing an agreement was in place. Koné looks the most likely solution to that problem heading into the new year, though prising him away from the Italian capital in the middle of a season will not come cheap.
Koné's contract with Roma runs until June 2029, giving the Serie A club a strong negotiating position and no obligation to sell at a reduced price, particularly with his stock continuing to rise the longer he remains a regular for both club and country.
Chelsea are not the only club to have shown interest in Koné this year, with the midfielder's combination of physicality, ball-winning ability and composure in possession having made him a target for several of Europe's leading sides. Roma's insistence on keeping him through last summer's window, even amid mounting interest, reflects how central he has become to head coach Gian Piero Gasperini's plans as the club looks to build on a positive start to the season.
Any move in January would represent a considerable outlay for Chelsea during a mid-season window, when fees for established performers typically carry a premium over what might be negotiated in the summer.