Speculation had suggested the 14-year-old had signed up with the west London outfit, despite previously undergoing trials at their local rivals Chelsea.
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"Contrary to reports, Brooklyn Beckham has been training at #QPR but has not joined our academy," the club tweeted.
Brooklyn started playing for fellow London side Spurs as a four-year-old and looks set to try to emulate his famous father’s career in football.
Beckham recently announced he will retire at the end of the season, ending on a high after helping Paris Saint-Germain win Ligue 1.