The Sky Blues are rumoured to be eyeing strike reinforcements in January, with manager Manuel Pellegrini concerned at a reliance on Sergio Aguero for goals.
With European hopes still high at the Etihad Stadium following last week’s stunning home win against Bayern Munich, City are keen to land a forward who will be eligible to represent them in continental football.
While a number of targets have already represented their clubs, Swansea’s lack of Euro action means that Bony is free to be registered for the latter half of the campaign.
While the Swans are keen to keep their man – who is set to represent the Ivory Coast at the African Cup of Nation’s in 2015 – offers of £20m are set to be tempting for them.
Liverpool were linked with Bony over the summer, and City will be buoyed by claims that the player was eager to leave the Liberty Stadium in search of bigger and better things.