The News of the World says the Brazilian demanded assurances from the City manager that he would play more in the build-up to the World Cup.
And Robinho made his final decision to leave for Santos on loan after being told he would only start in a third of City's games.
The striker, 25, had been advised by national team boss Dunga that he needed to play regularly to earn a place in Brazil's squad for South Africa.
"I was not playing at Manchester City, right?" said Robinho. "So I was honest with Mancini. I told him I want to play in the World Cup and that I have to play all the games I can until then.
"He told me he already has his team. I replied that I can't play one game and not play the next two, and he understood. Dunga's message to me was very clear - if I don't play regularly for my club side, then I do not go to South Africa.
"I will come back to City in the summer and prove that I'm not a player who sits on the bench.
"This is not just an escape from English football. I have thought about the move seriously and I thought I should have been in the starting team at City."