Zinedine Zidane is believed to be ready to offload the Colombian should a suitable offer arrive and Chelsea are ready to step up their interest.
Real Madrid enjoyed a phenomenal campaign last season as they won the Spanish Liga and Champions League.
In fact, James was so marginalised at the Santiago Bernabeu, he wasn't even named in the Real squad for the UCL final against Juventus.
On Saturday, rumours sprung up that James wants to sort out his future in the next 48 hours.
Madrid travel to the United States on Tuesday for their pre-season tour and Rodriguez is not planning on joining them.
United are among the frontrunners to secure the signature of the Colombia worldwide, and The Independent claims that the two parties are making progress in their discussions over a possible deal.
The 25-year old has always been linked with a move away from the Santiago Bernabeu, after having seen a major reduction in playing time since the arrival of manager Zinedine Zidane.
Liverpool, of course, are stocked with creative types in midfield, with Philippe Coutinho, Sadio Mane, Roberto Firmino and Mohamed Salah at Anfield.
Not many teams could afford James Rodríguez, especially if Real continue to insist on their current €70m asking price.
What's clear this weekned is that none of these clubs have so far tabled such an offer.