The 28-year-old, who Manchester United boss David Moyes attempted to sign in the summer, is not a guaranteed arrival at Old Trafford in January, with the Red Devils turning their attention to Porto's Alex Sandro.
Brazilian Sandro, 22, represents a younger and cheaper option for the champions.
That could leave the path clear for Manuel Pellegrini to secure the signature of the England international.
A Man City source said: "Baines fits the bill because he is English, familiar with the Premier League, defensively sound and a real attacking threat."