City signed the Ivory Coast international from their Premier League counterparts for £25m in January 2015.
A fee has not yet been agreed and talks may continue into next week but it is expected that Bony will return to the Liberty Stadium for less than half of that sum.
The 28-year-old made 46 appearances in his first 18 months at the Etihad Stadium, scoring 10 goals.
However, 26 of those appearances came from the bench and he was loaned to Stoke by manager Pep Guardiola last season.
Bony joined Swansea from Vitesse in 2013 and scored 25 goals in 54 games before joining City two and a half years ago.