Ari Emanuel, chief executive officer and executive chairman of TKO Group, UFC's parent company, outlined plans on ESPN's "The Pat McAfee Show."
"At the White House, I think it's 3,000 to 4,000 and then there will be others in other areas," Emanuel said.
Large screens to view the event were expected to be raised in other places near the White House for larger crowds to watch the show, which was also expected to be telecast on CBS and Paramount+.
Dana White, UFC's chief executive officer, is still working on the event, which is set to take place on the US Flag Day holiday and President Donald Trump's 80th birthday.
"Dana is working on it right now," Emanuel said. "There's going to be approximately six to seven fights on June 14th.
"He hasn't said to us what the card is going to be, but I know they are working pretty hard at it right now."