ESPN reported that LeBron was thinking about "walking away" from the sport after the Lakers' defeat brought the curtain down on his 20th season in the league.
Chris Haynes, a reporter for the TNT broadcaster, said in a separate tweet citing league sources that James's retirement was "under consideration."
LeBron himself fuelled speculation about his future in a cryptic post-game press conference, saying that he planned to take time to reflect on the next stage of his career after the Lakers' exit.
Asked for his reflections on the past season, where he became the league's all-time leading points scorer before leading a rejuvenated Lakers to the brink of the NBA Finals, James said the campaign had been "challenging."
"I don't know. I think it was okay. I don't like to say it's a successful year because I don't play for anything besides winning championships at this point in my career," said LeBron, who delivered a vintage 40-point performance in the Lakers' 113-111 loss on Monday.
"I don't get a kick out of making a Conference (finals) appearance. I've done it, a lot. And it's not fun to me to not be able to be a part of getting to the Finals.
"But we'll see. We'll see. We'll see what happens going forward. I don't know. I've got a lot to think about to be honest. I've got a lot to think about to be honest.
"Just for me personally going forward with the game of basketball, I've got a lot to think about."
LeBron signed a two-year contract extension with the Lakers last August that would keep him at the club through the 2024-2025 season.
'IT'S CHALLENGING'
He has long said that he wants to continue playing in order to play with or against his son Bronny James, who will play college basketball next season at the University of Southern California and could conceivably enter the NBA in time for the 2024-2025 campaign.
However, in his postgame remarks on Monday, LeBron hinted that the demands of the NBA's marathon 82-game season might be taking their toll.
"For me, it's all about availability for me and keeping my mind sharp and things of that nature, being present on the floor, being present in the locker room and bus rides and plane rides, things of that nature," LeBron said. "It's challenging."
There was little evidence of weariness, however, in LeBron's first-half performance on Monday, where he erupted for 31 points in a desperate bid to keep the Lakers' playoff hopes alive.
"That first half was vintage LeBron James," said Denver coach Michael Malone, who worked alongside LeBron as an assistant coach at the Cleveland Cavaliers from 2005 to 2010.
"Having coached him for five years in Cleveland, he understood what time it was with their team, firmly back against the wall," Malone said.
"In that first half he showed why he's one of the all-time great players, literally put his team on his back and just went at us."
Lakers defensive linchpin Anthony Davis, meanwhile, regretted that the team had not been able to give LeBron another crack at an NBA championship after the Denver loss.
"We know the window is always small and obviously he's not getting any younger," Davis said. "You know, this is why this was so important to both of us, and it hurts that we didn't get it done.
"But you know, we regroup, figure out ways we can be better."
