The two clubs are still locked in talks over the fee for the Ivory Coast striker, but City are ready to stump up the cash.
The Premier League champions will stagger the deal over a number of payments to help with their FFP restrictions, but will meet the total £30m that the South Wales club wants.
And Bony, 26, is set to sign a four-year deal at the Etihad on wages worth over £100,000-a-week.
City were prepared to go through January without making any further additions.
But they have decided to add to their firepower as they tussle it out with Chelsea for the title.
Star striker Sergio Aguero continues to be plagued by injury problems and boss Manuel Pellegrini fears the Argentine could be crocked once more during the title race run in.
Stevan Jovetic and Edin Dzeko have just 11 goals between them so far this season meaning City have been relying on Aguero.
The Argentina star has scored 19 goals so far this campaign, but has been out since the start of December with a knee ligament injury.
Aguero returned to training this week and could be back in action this weekend.
But with the Champions League returning in February, and the FA Cup to contend with, Pellegrini does not want to be short of attacking options.
Bony has scored 20 goals in the 2014 calendar year - more than any other Premier League striker.
He had been linked previously with moves to a number of clubs but signed a new deal in November with Swansea.
However, it appears that new deal has simply increased the Ivory Coast front man's value as his previous contract contained a £19m release clause.
The deal will smash the record transfer fee received by Swansea - the £15m they got for Joe Allen from Liverpool in 2012 the previous mark.
Despite being expected to agree the fee in the coming days, City will have to wait for at least three weeks until they can complete the deal as Bony is away with Ivory Coast at the Africa Cup of Nations.