The 16-year-old made his Premier League debut in the Hammers' shock 2-0 win over Arsenal on opening weekend in a defensive midfield role which allowed him to shackle Mesut Ozil and keep an eye on Aaron Ramsey.
Oxford was then substituted at half-time of West Ham's 2-1 defeat to Leicester City on Saturday but Upton Park legend Brooking knows the youngster has already done brilliantly well to achieve what he has in his fledgling career.
"For someone who's not even 17, he's done very well," Brooking told the Daily Mail.
"I joined West Ham at 16 and it was a couple of years before I made my debut."
And Brooking feels Oxford's future as in the centre of defence and not in front of the back four.
He added: "But I think long-term Reece will be a central defender. He's very tall and he's quick, but actually he will fill out a lot more.
"I don't think there is anybody at 16 who will be ever-present this season, so it's about trying to choose the moments when to play him.
"Sometimes as the anchor man in a midfield diamond, it's easier to play away from home than at home.
"At home, when sides come to sit a bit more, suddenly Reece might have the ball quite a bit where he's being looked to create or knock it into tighter areas."