According to the Guardian, Beckham made almost 400 appearances at United, winning the Premier League six times, the FA Cup twice and the European Cup.
Brooklyn, who was in the academy at LA Galaxy during Beckham's time in Major League Soccer, had a run-out with Chelsea at the start of the year before signing up for Queens Park Rangers' junior set-up, the report said.
Brooklyn''s desire to follow his father into football is well known, with bookmakers offering odds of 12-1 that he plays for England, and his visit to Manchester is aimed at measuring his ability and helping to find him the right environment, the report added.
Earlier this year, Beckham talked about the possibility of Brooklyn, or one of his other sons, becoming a footballer, according to the report.
He said that as a parent, one always worries whether their children have the same hunger that he had as a kid, adding that he is hard on his boys just as his dad was.
Beckham said that his kids always ask him whether they played well and he says that they did all right but could have been better.