Walton has come under huge pressure this season as his side have made a poor start to the new campaign.
The Lakers have won just three of their opening eight matches, despite the blockbuster signing of James in the summer.
Magic Johnson convinced the small forward to put pen-to-paper on a four-year deal after leaving Cleveland Cavaliers.
But his arrival was supposed to help the Lakers’ young players develop into a play-off contending team.
Walton’s side has yet to click into gear and if the head coach is axed then 2011 NBA champion Jason Kidd has been tipped to take over.
Kidd has most recently been in charge of Milwaukee Bucks and James is said to be an admirer of the 10-time All-Star.
“LeBron James always wanted to play with J-Kidd,” an NBA league source told Brandon ‘Scoop B’ Robinson.
“This would probably be the next best thing to that.
“Anything is possible in this league.”
Meanwhile, James believes his team is making small steps towards their goal after beating Dallas Mavericks 114-113 last time out.
“I liked the way we played,” James said.
“I don’t like the way we closed out the game but for the majority we played well.
“We took our foot off the gas and allowed them to get back into it, they were getting into a great rhythm.
“I made a dumb mistake. The cardinal sin is to give a three when up four so I can’t stand myself for that. That just can’t happen.”
The Lakers are next in action away to Portland Trail Blazers tonight.