Beckham senior, who began his career by joining Manchester United's academy also at the age of 14, retired from the game last week after helping Paris St Germain to the French league title but now has a home in London.
Bookmakers are offering odds of 12-1 that Brooklyn will play for England but only 9-2 to play in the Premier League.
QPR were relegated from the Premier league this season.
In other celebrity English soccer news on Tuesday, Manchester United announced that their unsettled striker Wayne Rooney had become a father for the second time with boy Klay joining brother Kai.