The son of David Beckham joined the Bees’ B team on loan in January from MLS side Inter Miami II, the franchise owned by the former Manchester United star.
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Beckham, 20, helped the B team win the Premier League Cup and left a good impression on Brentford B boss Neil MacFarlane.
The winger was expected to return to Miami after his six-month loan spell ended.
However, ongoing talks could see Beckham remain at the Gtech Community Stadium, according to the Daily Mail.
The report does not specify if it would be a permanent switch or another loan.
However, MacFarlane insisted that he is more than happy to continue working with the youngster.
MacFarlane told the Daily Mail: “He has been a pivotal member of what has been a special group this year.
“There will be a decision made on Romeo.
“I have no qualms in putting my name to him – I want to help his development again.
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“I’d have no problem whatsoever if he was to stay here and we continue his development at Brentford.”
Should Beckham return to Brentford, he would likely join back up with the B team.
It is thought that he would be keen on a London stay as he could be closer to partner Mia Regan.
The showbiz pair have been dating for three years after first meeting in September 2019.
Romeo had even sparked engagement rumours when pictured with his model girlfriend as she flashed a huge diamond ring.
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