Kone, currently on international duty with France at the World Cup, is viewed by United's recruitment staff as a genuine alternative rather than merely a fallback option, with the club moving quickly to open the door on a deal once the Ederson situation turned sour.
AS Roma value Kone highly given his importance to Gian Piero Gasperini's midfield, but a bid in the region of €50million would represent a significant offer that the Giallorossi may find difficult to turn down outright.
The shift in target comes after United's move for Ederson collapsed, despite an agreement worth €45million plus €3million in bonuses having been in place between the two clubs for some time. According to reports in Italy, United's decision followed a more thorough round of medical examinations, with the club's staff ultimately concluding that the Brazilian was not as fit as they had expected.
Atalanta, by contrast, consider Ederson to be in good health and will welcome him back into the squad, where he will be available to new head coach Maurizio Sarri.
The timing of United's withdrawal has raised suspicions in Italy, where some reports suggest growing interest in Kone may have influenced the decision to walk away from Ederson rather than any genuine medical concern.
Some sources close to United have pushed back on the suggestion the Ederson deal is definitively off, insisting internally that the situation remains under review, though the prevailing reporting in Italy treats the move as dead and United's focus as having already shifted to Kone.
Signing both players in the same position would represent an unusually heavy outlay for a single role, making it more likely United's midfield rebuild will ultimately centre on Kone alone, alongside the previously agreed signing of Andrey Santos from Chelsea, as United continue reshaping their midfield following Casemiro's departure as a free agent at the end of last season.