"He was there with his dad and took part in a practice session with one of the academy sides," a source at the club told the Manchester Evening News.
"It was a chance for him to impress and if he's done well then no doubt the club will look at taking him on."
The 14-year-old was accompanied by his former England caption dad at the training session at the club's facility in Carrington.
An onlooker disclosed that Brooklyn played on the right wing and "impressed spectators" with his display.
Brooklyn, who is said to be an Arsenal fan, played for LA Galaxy's youth team while his famous father was based at the club.
He also had a trial with British team Chelsea in January before going on to sign for QPR's youth system in May.
Brooklyn's not the only upcoming football star in the family - younger brother Romeo, 12, was recently signed by Arsenal for their youth academy.
Romeo also recently made his debut in the fashion world with a modelling campaign for Burberry.