The Afrobasket tournament starts in Rwanda on August 24, two weeks after the Olympics end in early August in Tokyo, which would trigger an NBA rule prohibiting Nigeria's players from too much international game time.
Brown, an assistant coach with the Golden State Warriors, told ESPN: "It is my understanding that NBA players that play in the Olympics won't be able to play in the AfroBasket because they can only play a certain number of days of international competition in a year.
"For the days of training per year, I'm not sure there is a limit of days per year, but there is usually a limit of 28 practice days leading up to the Olympics and World Cup competitions.
"If there are two significant competitions in one year, like the Olympics and AfroBasket, NBA players are often limited to participate in only one of those competitions."
This means Brown could be forced to form two teams, of equal strength, to compete for two medals just weeks apart. D'Tigers are ranked 22 in the world by FIBA, so aren't just making up the numbers in Tokyo, while they're former Afrobasket champions and tanking there isn't an option either.
Brown said: "Yes, there could be two teams. But we have not decided who will be on the roster yet so that decision is still some way off."
As for which players could be affected by this rule, it's an ever-increasing list as players eligible for Nigeria, by birth, parentage, or naturalisation, pick D'Tigers over other options.
From the NBA comes not just veteran campaigners like Al Farouq Aminu, Chimezie Metu, Josh Okogie, Jordan Nwora, and Gabriel Vincent, but newbies like the rookies drafted in the 2021 class. This includes Precious Achiuwa, Zeke Nnaji, Udoka Azubuike, Aaron Nesmith, and Desmond Bane.
They could also be joined by the potential naturalisations of Denver Nuggets' Monte Morris and Brooklyn Nets' Spencer Dinwiddie, if he can get back from injury ahead of schedule to play a part in the Nets' Playoff run.
Brown says he has made no decisions about which players are going to be selected until they get to training camp.
"Right now, nobody has been picked yet. We will have to go to training camp, look at everyone and then make the best decision about who goes where to give us the best chance of winning at both tournaments," he said.
Difficult as that selection job will be, NBBF President Musa Kida insists that the selection will be done on merit.
"This is the golden era of Nigerian basketball," Kida told ESPN. "Many high profile players who would have turned us down in the past if invited, are now hustling to get our attention, and that is a good thing for us.
"All eligible players have an equal chance of getting invited to camp and making the final list. And it will be up to the coaching staff to select the best because they are in the best position to do so."
Nigeria became the first country to qualify for the Afrobasket and they did so in some style, winning all six qualifying games over two windows.
Last week, the draws for the AfroBasket were made in Rwanda. D'Tigers - Africa's top-ranked team, were placed in Group C with Cote d'Ivoire (ranked 50th, and 5th in Africa), Mali (ranked 77) and surprise package Kenya (ranked 112 and 19th in Africa).
For the Games in Tokyo, Nigeria -- currently on a nine-match winning streak -- open their Olympic campaign on July 29 against number 3-ranked Australia in a group B fixture at the Saitama Super Arena in Tokyo.
Mike Brown targeting a medal with Nigerian Olympic team
Olympic basketball coach Mike Brown wants to show that Nigeria "can compete with the best" in 2021.