The NBA stars were among 30 players selected Monday as finalists for the U.S. basketball team that will compete in Rio de Janeiro and attempt to win a third straight gold medal.
The final 12-player roster will be chosen this summer. If James and Anthony are on it, they would become the first American men to play in four Olympics.
The other candidates for Rio are: Kevin Durant and Russell Westbrook (Oklahoma City Thunder); Chris Paul, Blake Griffin and DeAndre Jordan (Los Angeles Clippers); Kawhi Leonard and LaMarcus Aldridge (San Antonio Spurs); Klay Thompson, Draymond Green, Andre Iguodala and Harrison Barnes (Golden State Warriors); Kyrie Irving and Kevin Love (Cleveland Cavaliers); Dwight Howard and James Harden (Houston Rockets); Anthony Davis (New Orleans Pelicans); Paul George (Indiana Pacers); DeMarcus Cousins and Rudy Gay (Sacramento Kings); John Wall and Bradley Beal (Washington Wizards); Jimmy Butler (Chicago Bulls); Mike Conley (Memphis Grizzlies); DeMar DeRozan (Toronto Raptors); Andre Drummond (Detroit Pistons); Kenneth Faried (Denver Nuggets); and Gordon Hayward (Utah Jazz).
"The depth of talent that exists in the national team program is extraordinary. Repeating as gold medalists at the 2016 Olympics will not be easy, but we feel confident that we have 30 finalists who offer amazing basketball abilities and special versatility," USA Basketball chairman Jerry Colangelo said in a statement.
Kobe Bryant, who is retiring after this season, took himself out of the running for a third Olympics this weekend.
James and Anthony, who won bronze in 2004 before leading the U.S. to gold in Beijing and London, have already joined Hall of Famer David Robinson as the only U.S. men to play in three Olympics. Paul could join that list this summer.
James has said he would base his decision about playing on his health and his family's wishes, and may not decide until after his NBA season ends.
"I haven't thought about it," he said at Cleveland's shootaround before its game against Golden State on Monday.
"The last time I thought about Team USA was Kobe taking his name out of the pool. That's the last thing I kind of really thought about, so I'm not any inch closer to playing or not any inch closer to not playing. I haven't really thought about it much."
James has played in five straight NBA Finals, and another lengthy season could affect his interest in wearing the red, white and blue again.
"The season has always kind of dictated it," James said.
Curry called it a huge honor to be selected.
"That would be a great experience,'' Curry said following Golden State's 132-98 victory at Cleveland. "Obviously, there's 30 capable, highly talented experienced guys on that list. There should some tough decisions for Mr. Colangelo and Coach K. Picking from that crop of 30 guys you've got some great choices there. Hopefully things work out this summer and I'll be able to try to go for a gold medal in Brazil.''
Colangelo has said the Americans could send their strongest team yet to the Olympics, and it could certainly be their most experienced one. The pool of finalists includes 18 players who have won Olympic or world championships, and seven players who have played at least 30 international games -- led by Anthony's 72.
Like James, Anthony isn't ready yet to commit to playing again.
"This summer's a long way away for me to be thinking about that right now,'' he said after returning from a two-game absence due to a sprained right ankle and playing 49 minutes in the Knicks' double-overtime victory over Philadelphia.
George, who suffered a fractured leg during a Team USA scrimmage and missed almost the entire 2014-15 NBA season as a result, also was noncommittal.
"I'm still happy to have a chance. It's definitely a dream to be a part of that group but we'll see," George told reporters. "It's been a long year for me already so we'll see when it gets down to being there. I'll listen to my body and listen to the trainers to see what's the best move."
Ten players have suited up for the Americans in the Olympics, but Curry isn't among them. He wasn't chosen for the team in 2012, shortly before the NBA's MVP broke out as one of the game's biggest superstars.
He won gold medals in the 2010 world basketball championship and 2014 Basketball World Cup and will be a strong candidate to make the Olympic team now even in a crowded point guard field that includes Paul, Westbrook, Irving -- the MVP of the World Cup in Spain two years ago -- Wall and Conley.
"This selection process was difficult from the start, and obviously it is only going to get more difficult as we look to get to the official, 12-man roster," U.S. coach Mike Krzyzewski said. "I'm excited about the possibilities this team has."