The Sky Blues have made the Ivorian forward their top January target, with talks between the Premier League rivals having been on-going for the past few days.
But, with Swansea holding out for £30m for their man, the deal has hit a snag.
City are desperate to get Bony in to boost their title charge, but Financial Fair Play punishment lobbied by UEFA limits them to a net spend of £49m this financial year.
While more than transfers alone are factored into this, the defending champions have already splashed £40m on Eliaquim Mangala, £12m on Fernando and a further £4.4m on Willy Caballero – albeit some of this has been recouped by the sales of Javi Garcia and Jack Rodwell.
As a result, City are keen to get a deal done on their terms, which has frustrated Swansea – who are in no desperate hurry to sell the Premier League’s top scorer in 2014 the 26-year-old netted 20 goals.
Personal terms are expected to be a formality between the marksman and the club.