The 26-year-old is on international duty with Ivory Coast at the Africa Cup of Nations.
The Ivory Coast Football Federation said: "Bony has signed with Manchester City this Wednesday, 14 January."
But a Swansea spokesman responded: "The club has not confirmed anything and the Ivory Coast have no right to comment."
The club added on Twitter that Bony "has NOT yet completed his move" and when he does, it will be confirmed "via official channels - not the Ivory Coast FA".
The two clubs agreed a £28m deal for Bony at the weekend, with £25m cash up front and a further £3m in performance-related add-ons.
Bony joined Swansea for a club-record £12m from Vitesse Arnhem in 2013 and was the Premier League's top scorer in 2014 with 20 goals.
He has scored nine times in 22 appearances this season.
He was the Premier League's top scorer in 2014 with 20 goals and has scored nine times in 22 appearances this season.
Wilfried Bony
