"We thought they were serious," one insider told the Daily Mail last night. "However, they acted as if this was just a game.
"We are sure the owner will not be impressed when he learns of this development."
City denied the claims from Italy.
An first meeting involving Milan officials and Kaka's management team was said to have been "difficult".
A second round of talks were planned for today with City preparing to make their official offer to the player, previously reported to have been worth around £500,000-a-week.
Their approach yesterday, when they failed to talk money with Kaka's father, are said to have "surprised and disappointed" the Brazilian's negotiating team.
Soon after the meeting broke up, Kaka withdrew from the transfer.