The 26-year-old, who has scored nine goals in 22 appearances this season, is on international duty at the Ivory Coast training camp in Abu Dhabi ahead of the African Cup of Nations which starts in Equatorial Guinea on Saturday.
The Ivory Coast Football Federation said on Twitter: "Bony has signed with Manchester City this Wednesday, 14 January."
But Swansea quickly responded saying, "The club has not confirmed anything and the Ivory Coast have no right to comment."
The club added that Bony "has NOT yet completed his move" and that when he does, it will be confirmed "via official channels - not the Ivory Coast FA".
Swansea and City reportedly agreed the deal for Bony at the weekend. The player joined the Swans for a club record 12.0 million pounds fee from Dutch club Vitesse Arnhem in 2013.
(Reporting by Mike Collett, editing by Alan Baldwin)
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