Rodriguez returned to the Santiago Bernabeu at the beginning of the season following a loan spell at Bayern Munich, but was expected to move on again after initially not being part of Zidane's plans for the club.
Those plans changed following a spate of injuries to key players, however, which prompted James to stay at Real, where he is now fighting to cement a place in the starting XI.
According to AS, the 28-year-old is hoping to earn Zidane's favour and has elected not to travel with the Colombia squad for their friendlies against Chile and Algeria in a bid to establish his place at Real.
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Rodriguez reportedly asked national team coach Carlos Queiroz for time away during this international break in order to continue his reintegration into the Los Blancos squad.
The decision is said have sparked controversy in his native Colombia, where supporters are upset that the 76-cap star has elected to choose his club over his country.
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Rodriguez has scored one goal and assisted one further strike in seven appearances for Real so far this season.
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