The 26-year-old has been with the Liberty Stadium side since making a club-record £14 million move from Dutch outfit Vitesse Arnhem in 2013.
Just seven weeks ago Bony extended his deal with Swansea until 2018, but the Ivory Coast international is now close to leaving south Wales for the Etihad Stadium.
The striker’s agent, Francis Kacou, expects “things will be sorted in the next few days”, allowing the reported £30 million deal to be completed.
For the time being talks remain ongoing and Bony, who is jetting off to Abu Dhabi ahead of the African Nations Cup, is excited by what a move to City would bring.
“It is going well,” Bony told Sky Sports News. “The discussion is still on. I am now going to join my national team so I am just focused on that.
“Every player wants to play Champions League, World Cups. It is the wish of every player.
“When you get the opportunity… sometimes good ones, sometimes not, but I am just taking it step by step.
“I am focusing on my national team and wait to see the news like you.”
Bony has yet to have a medical with City and his agent confirmed there are “some small details about money” to sort out.
Reports suggest he will pen a four-and-a-half-year deal worth £100,000 per week, with the striker eligible for Manuel Pellegrini’s side in both the Champions League and FA Cup.