Chelsea been tracking Robinho for much of the summer and lodged a bid with Real earlier this month.
The 24 year old is desperate to leave the Bernabeu and secure a move to Chelsea, and Real responded by saying they would let him leave.
Agent Wagner Ribeiro expects the matter to be resolved before the close of the transfer window.
"The deal is about to be reached," Ribeiro said in the Daily Mirror.
"Robinho's cycle in Spain has come to an end and he is looking forward to a new project."
Reports suggest that Robinho will travel to London this week to discuss personal terms ahead of a proposed £28million move.