The Brazil is now believed to be upset with the club directors after they refused to allow him to represent his country in the Beijing Olympics.
"It's not my objective to continue at Real Madrid," he said in remarks reported by Brazilian website globoesporte.com.
"I highly respect the club, the players, and especially the fans, who've always treated me well, but that's not my objective.
"I have an offer (from Chelsea) which is good for me and the club. I dream of playing in the English league.
"Chelsea have a great squad and a great team. My objective is to play there.
"I've got nothing against Real Madrid, but I hope to resolve this situation as soon as possible."
Robinho insists money is not a factor in his decision to leave.
"It's not about money, I simply want to leave," he said.
"I want to be the best player in the world and that isn't possible at Real Madrid.
"I've come to an end of a cycle. I've played three seasons at Real Madrid, I've given my all. I've scored goals, I've won two leagues, and that's not easy.
"I think that my time here has now come to an end."