The Colombian international moved to the Bernabeu after claiming the Golden Boot award at the 2014 World Cup with six goals – including a strike against Uruguay that later won the 2014 Puskas award.
The attacking midfielder initially impressed in the Spanish capital but seriously struggled for fitness and form last season, making just 17 starts in La Liga.
El Confidential claim Real Madrid are ready to cut their losses on the 24-year-old, provided a club repays the £65million investment they made in Rodriguez two summers ago.
And two Premier League clubs have already made contact in an effort to negotiate a deal for the South American – title chasers Chelsea and Manchester City.
However, French champions PSG are also chasing Rodriguez and have reportedly already registered their interest with his representative – the renowned Jorge Mendes.