Kone's immediate future is set to remain in the spotlight following the conclusion of the World Cup, where he will still have a third-place play-off to complete with France after their semi-final exit to Spain.
Speaking on his YouTube channel, Ferdinand claimed the move was already done, citing information from transfer journalist Fabrizio Romano.
"Manchester United have reached an agreement for Kone and will pay 53 million euros," Ferdinand said, adding that the midfielder would be a strong fit for Michael Carrick's 4-2-3-1 system.
Romano himself, however, has so far described the situation in more measured terms. In recent public updates, the journalist has said Manchester United made contact with Kone's representatives as one of several names under consideration for a third midfield addition this summer, rather than confirming an agreement is in place.
United have already strengthened their midfield significantly this window, having completed deals for Youri Tielemans and Andrey Santos, but are said to be seeking a more defensive-minded option to eventually succeed the departed Casemiro. Kone, 25, has been one of the standout performers at the World Cup and has three years remaining on his contract in the Italian capital.
AS Roma's precarious financial position has fuelled speculation that a sale involving one of their key players may be required this summer, with reports in England suggesting a fee in excess of £45m would be needed to prise the France international away from Trigoria.
Roma sporting director Tony D'Amico is understood to be exploring both incoming and outgoing business over the coming days, with Gian Piero Gasperini having hinted previously that a significant departure from the squad may be necessary this window.
Whether Ferdinand's claim of a completed agreement proves accurate remains to be seen, though it adds further intrigue to a deal that has been gathering momentum for weeks.
Kone has three years remaining on his contract in the Italian capital and has established himself as one of Roma's most important midfielders since arriving from Borussia Monchengladbach, making his potential departure a significant call for the Serie A club as they plan for the season ahead.