Liverpool and Manchester United are set to go head-to-head to sign Rodriguez at the end of the season.
The Colombia international has grown unsettled under Zinedine Zidane this season and Spanish newspaper Marca claimed Rodriguez called the Real Madrid boss a "motherf****r" after being subbed against Leganes.
Rodriguez joined Real in 2014 after starring in the World Cup in Brazil for his country.
Real Madrid will sell James Rodriguez, according to Guillem Balague
Jurgen Klopp is reportedly interested in bringing Rodriguez to Anfield
But the midfielder has struggled to build on his impressive debut campaign at the Bernabeu, in which he scored 17 goals and assisted 18 in all competitions.
"Real Madrid want to sell him and about €35m would do it," Balague told Sky Sports.
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Manchester United are favourites to sign him, according to Balague
"All the options remain on the table – Manchester United and Liverpool want him – but I just think United have the edge if it comes down to those two clubs. Jorge Mendes is his agent.
"But Italy is an option too. The only guaranteed thing at this stage is Real Madrid want him to go and he is considering his options."