Reports has linked City with a £10million bid for the 26-year-old Brazilian superstar.
“We believe the deal is very close,” said Bowen to BBC Sport Wales. “We are selling the future plans of the club to the player.
“I’ve read a lot about his love of Milan – and that goes without saying – but even when people said the deal was dead that was not our understanding.”
“We are still hopeful of signing Kaka,” added Bowen. “The situation has been a surprise to everyone but obviously negotiations have been going for a fair while.
“How close we are I don’t know, but our understanding is that it is very much a strong possibility that Kaka will be coming to Manchester City.”