The former striker, who played on both sides of the Manchester divide but is best remembered for his successful spell at United, has made his bold claim despite the Blues' rise to joint top of the Barclays Premier League table.
Victory at West Ham saw Mario Balotelli substituted to stop him getting himself sent off - followed a day later by confirmation that Carlos Tevez wanted to leave, triggering a downward spiral in the club's relationship with their captain.
It all paints a pretty sorry picture, which Cole is convinced will lead to their championship challenge fading.
"There are a lot of problems there," he said.
"Anyone who has any common sense and understands football knows that.
"You can't have disputes with the manager at such regular intervals.
"Every other week someone is coming out saying they are not happy. You can't run a tight ship like that.