James said he would be OK with Stephenson as a teammate.
"I just want to win, man," James said after the shootaround as the Cavaliers prepared for their home game against the Minnesota Timberwolves on Wednesday night. "That's all that matters to me. I got no personal problems with nobody."
"I got a history with all those guys except Jordan," James said. "I got a history with Lance too, obviously. I got a history versus Kirk. I played him in a lot of playoff series. And I got a history with Rio (Chalmers). ... At the end of the day, Rio is recovering from his Achilles tear. I hope he's been doing everything he needs to do just to get back on the floor. He loves to play the game.
"I'm a supporter of what this franchise wants to do, no matter what it's doing. But my focus right now is to get our guys playing championship-level basketball."
Stephenson was on the Pacers teams that the Heat faced in the playoffs for three consecutive postseasons from 2012 to 2014.
Stephenson averaged 9.7 points, 4.8 assists and 3.0 rebounds for the New Orleans Pelicans in six games this season before needing groin surgery. He was cut by the Pelicans in November.
James played four seasons in Miami with Chalmers as the Heat's primary starting point guard. They reached four NBA Finals and won two championships together.
Chalmers, a nine-year veteran, has career averages of 9.0 points, 3.8 assists and 1.5 steals. He suffered an Achilles injury while playing for the Memphis Grizzlies last March.
Meanwhile, a day after James called him a "hater" and dug up some of his personal history, TNT analyst Charles Barkley said he stands by his criticism of James.
"I stick by what I said, I'm not going to make this personal. ... He was all whiny last week," Barkley said Tuesday on ESPN Radio. "I'm good and I'm straightforward, I'm never going to get personal on an NBA player."
Barkley said James was being "whiny" for publicly saying the Cavaliers needed to bring in another playmaker.
"Inappropriate. Whiny. All of the above," Barkley said of James last week. "The Cleveland Cavaliers, they have given him everything he wanted. They have the highest payroll in NBA history. He wanted J.R. Smith last summer, they paid him. He wanted (Iman) Shumpert last summer. They brought in Kyle Korver. He's (LeBron) the best player in the world. Does he want all of the good players? He don't want to compete? He is an amazing player. They're the defending champs."
James fired back, maybe taking out his frustrations after the Cavaliers' 7-8 January.
"I'm not going to let him disrespect my legacy like that," James told ESPN. "I'm not the one who threw somebody through a window. I never spit on a kid. I never had unpaid debt in Las Vegas. I never said, 'I'm not a role model.' I never showed up to All-Star weekend on Sunday because I was in Vegas all weekend partying.
"All I've done for my entire career is represent the NBA the right way. Fourteen years, never got in trouble. Respected the game. Print that."
Barkley, who was asked whether he felt James crossed the line, said he had no issues with the superstar's remarks.
"I was laughing, clearly he did some homework ... he Googled me and found some things," Barkley said. "He was young when I was playing, so I appreciate that, but I'm not upset about it. ... My criticism was fair, and I'm good with that."