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The 29-year-old Colombian, a favourite of Toffees boss Carlo Ancelotti, has had a bright start to his football career in England.
However the British weather and the "very physical football" in England are allegedly not to his liking. Rodriguez has had to handle a couple of niggling problems with his calf and groin this season and he is said to be concerned about the amount of injuries he's picking up.
According to Spanish media source Defensa Central, Rodriguez would ideally like a return to the city of Madrid.
However rather than his former club Real Madrid, the Colombian would prefer to go to their crosstown rivals Atletico Madrid.
The attacking midfielder signed for Real Madrid for £63 million from Monaco after his star-making turn in the 2014 World Cup.
But he spent two years out of six on loan at Bayern Munich and never strongly featured in current Real manager Zinedine Zidane's plans.
That led to the free transfer to Everton this summer which looked an ideal move, as it linked Rodriguez up with his former Real and Bayern coach Ancelotti and gave the Merseyside club a fresh attacking impetus.
Rodriguez himself has said nothing at this point and seems committed to Everton's cause on the pitch, having scored five goals and registered seven assists since his arrival in September.
However he would not be the first South American footballer to find the transition to England's top flight a challenge. The climate, style of football, language and culture is very different to that of South America or of Spain.
Everton have also been linked with another attacking midfielder this summer: Juventus's French international Adrien Rabiot will reportedly be the subject of a £26 million bid, according to The Sun.
We'll just have to wait and see whether that could be a replacement for an outgoing James Rodriguez - and whether a move to Atletico Madrid and a link-up with Diego Simeone is in fact of interest to both the player and the clubs involved.
All imagery: PA Images
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