AS.com said the Colombian was chased to the training ground gates by an unmarked police car that had repeatedly signalled for him to pull over.
The speed limit on the roads he used was 120 kph.
Rodriguez could face a hefty fine and have his licence taken away, as happened to team mate Karim Benzema last year.
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There was no immediate comment from the player or Real Madrid.
(Writing by Mark Meadows; Editing by Tony Jimenez)
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