Reports earlier today had claimed that the 23-year-old had informed his current club Monaco of his desire to sign for the 10-time champions of Europe.
There has been no official word from either club, but following his presence, which has been captured by numerous shots on social media, in the Spanish capital this afternoon, it has been suggested that a deal is near to a conclusion.
James en Madrid. pic.twitter.com/GEdG5ovUfq— FútbolSocial (@FutbolSocial) July 20, 2014
A bit later, the striker was then pictured on the Madrid Metro, believed to be heading for the city centre.
James, en el metro de la T4 pic.twitter.com/13Ut7wEY3D— Míchel Martín (@michel_martin) July 20, 2014
It has been claimed that Los Blancos will pay their Ligue 1 counterparts around £70m for Rodriguez's services.