The Argentine defender is set for talks with Real after the Spanish giants agreed a deal with Manchester United for the player just 24 hours after the Premier League blocked Heinze's move to Liverpool.
"It has been complicated. I am convinced my move to Liverpool would have worked out and I believe I had a case and needed to defend my rights," Heinze told the Daily Mail.
"I am grateful for what Rafa Benitez said and tried to do.
"I didn't want more controversy with Sir Alex Ferguson.
"It is logical now for me to make this jump.
"I always said I wanted to leave for one of the big clubs in Europe and Real are one of those."