USA Basketball officials have one month and one day to submit their final Olympic men’s roster after winnowing down a field of 57 finalists to 12, but exactly who will play for the United States at the Tokyo Games remains a mystery.

LeBron James, for one, all but ruled himself out after the Los Angeles Lakers’ season-ending 113-100 loss to the Phoenix Suns on Thursday night, reminding everyone he has a “Space Jam” sequel to promote this summer.

Los Angeles Lakers forward LeBron James signals to a teammate during the first half of an NBA basketball game against the Charlotte Hornets on Thursday, March 18, 2021, in Los Angeles. AP Photo/Marcio Jose Sanchez

“I think I’m going to play for the Toon Squad this summer instead of the Olympics,” James said after the Lakers’ 113-100 loss to the Suns. “I think that’s what my focus (is) on, trying to beat the Monstars, or the Goon Squad we call them now. So, didn’t have much success versus the Suns, so now I am gearing my attention to the Goon Squad here in July, mid-July.”

James hasn’t played for Team USA at the Olympics since the 2012 London Games, and at 36 he would be the oldest player ever to suit up for the U.S. Olympic men’s basketball team. James also is dealing with an ankle injury that he called “the most important thing” he’ll have to deal with this summer (besides promoting his movie, which also seems to be a big offseason priority).

“I’m going to let the ankle rest for about a month and then gear up with Lola, Taz, Granny, Bugs and the rest of the crew,” he said, referencing some of the animated characters in the movie.

Stephen Curry never has played in the Olympics, sitting out the Rio Games four years ago after helping lead the Golden State Warriors to another NBA Finals. But after a bounce-back season in which he won the NBA scoring title, the 33-year-old Curry seemed unsure of his Olympic participation when asked about it after Golden State’s season ended two weeks ago.

“Obviously everything was geared towards extending this season as far as possible, and honestly, I know there’s a lot of conversation and chatter about logistics and the set up and all that type of stuff, I don’t know what that looks like from Team USA, so trying to gather as much information as possible and make the right decision for me at the end of the day,” Curry said.

With the NBA season pushed back and the Olympics postponed because of the coronavirus pandemic, logistics are indeed an issue. The July 5 deadline for Olympic rosters to be submitted falls three days before the NBA Finals are scheduled to begin, and USA Basketball will hold minicamp and training camp in Las Vegas before the deadline. That means players from the four teams that reach the NBA conference finals are almost certain to be unavailable for the Olympics, further winnowing the field.

USA Basketball men’s national team director Jerry Colangelo told USA Today last week that the process will begin in earnest after the first round of the playoffs, which will end either Friday or Sunday.

“I’ll cut to the chase because people are asking me, ‘A lot of teams are out (of the playoffs) — are you going to get early commitments from certain people?'” Colangelo said. “That’s not the way we’re going to deal with this. We have interest in all of them. There’s a lot of variables, and so we’re going to do inventory after the first round. There’ll be a number of players who we have interest in that conceivably are available after the first round. There’s no rush because we have the flexibility.”

Of the 57 finalists announced by USA basketball, 16 play for teams that already have advanced to the second round of the NBA playoffs and another two play for the Los Angeles Clippers, whose first-round series against the Dallas Mavericks has yet to be decided (Dallas does not have any Olympic finalists on its roster).

Those 18 players: Mike Conley and Donovan Mitchell (Utah); Devin Booker and Chris Paul (Phoenix); Blake Griffin, DeAndre Jordan, Kevin Durant, James Harden, Joe Harris and Kyrie Irving (Brooklyn); Brook Lopez, Khris Middleton and Jrue Holiday (Milwaukee); Trae Young (Atlanta); Tobias Harris and Dwight Howard (Philadelphia); and Paul George and Kawhi Leonard (Los Angeles Clippers).

Eight other finalists already have said they will not be playing in the Olympics or have suffered injuries since the list was released in March, including the Lakers’ James and Anthony Davis (who was hobbled by a groin injury against the Suns); the Celtics’ Jaylen Brown (who suffered a wrist injury near the end of the regular season and is out at least three months); the Hornets’ Gordon Hayward (who sprained his foot in April); the Rockets’ John Wall (the injury-plagued star whose season ended early because of a hamstring tweak); the Pacers’ Myles Turner (who suffered a season-ending toe injury in April); the Pelicans’ Zion Williamson (who fractured his left ring finger in early May); and the Knicks’ Mitchell Robinson (who had surgery on his broken foot in late March).

That leaves 31 finalists who are healthy, seemingly available and no longer playing with their NBA teams this season.

“It’s conceivable, there will be a few players who are competing in the Finals and want to participate, and we want them to participate,” Colangelo told USA Today. “But we don’t know who that’s going to be. We have to wait and see. That’s why we’ll take inventory after each round. It’s possible that we don’t end up with 12 in Las Vegas and we bring a couple of guys at the last minute.”