Briton Norris, the 17-year-old star of European F3, is tipped for a bright future in F1 and already firmly under contract to McLaren.
Brown has said that McLaren are likely to place Norris in Formula 2 next year, rather than seriously consider him as a potential replacement for Fernando Alonso.
Yet as the standout F3 star, other F1 teams may be interested in offering Norris a 2018 seat.
"No team has made a request so far, and our current plan is to let him compete in Formula 2," Brown is quoted as saying by Speed Week.
"He's definitely our star of the future, so I do not think we're giving him to another team.
"I am convinced that he is fast enough to compete in formula one now, but we also have to ensure it's not too soon for him and he gets enough experience."
McLaren are ninth in the team rankings ahead of this weekend's Singapore Grand Prix.