According to various reports, the two clubs have already agreed a fee of around €80m (£63.4m) and the player has agreed a six-year contract worth €7m (£5.5m) a season.
James caused a flurry of excitement when he flew into Madrid on Sunday evening from Colombia but he never left the airport and instead took a connecting flight to Nice.
He will stay in Monaco waiting for the transfer to be officially completed before being unveiled at the Bernabeu.
It is believed the only outstanding issue in regards to the transfer is whether any Real players will be sold to Monaco as part of the deal.
According to AS, Monaco are keen to sign goalkeeper Diego Lopez but the player is reluctant to leave.
Real would likely be willing to allow Lopez leave as they are also on the brink of signing Costa Rica goalkeeper Keylor Navas from Levante
German midfielder Sami Khedira is another player who has been mentioned as a potential make-weight in the deal.
Real could also recoup around €50m (£39.6m) of the transfer fee by selling Angel Di Maria to Paris St Germain although Financial Fair Play issues for the French club complicates that transfer.
James is set to wear the number 10 shirt that has been vacant since Mesut Ozil left the club for Arsenal last summer.
James won the golden boot at the World Cup after scoring six goals in five games and many felt he was unfairly overlooked for the player of the tournament award which instead went to Argentina's Lionel Messi.
Well it looks like Real Madrid have done it again and signed another superstar to add to their ranks. James certainly looks the real deal and after only turning 23 a week ago – has plenty of time to get even better. With Toni Kroos having also signed for the Bernabeu club and Luis Suarez having moved to Barcelona, the two Liga giants have really flexed their muscles this window after seeing Atletico crash their domestic party last season. The prospect of this season's Clasico clashes already have the mouth watering.
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