The Colombian has fallen down the pecking order under Zinedine Zidane and he is reportedly ready to leave the Spanish capital.
A number of Europe’s big clubs are now on red alert, including French champions Paris Saint-Germain.
However, according to Sport, the most concrete interest in James is coming from Chelsea.
The Premier League side are still hoping to do business before the transfer window closes next week and they have money to spend.
Despite James’ failure to nail down a first-team spot, Real Madrid would still demand around £60million for the attacking midfielder.