"I'm optimistic about life," Walton said in response to questions about James' recovery, according to ESPN's Ohm Youngmisuk. "So yes, that would be covered in that.
"I think we'll get good news back."
James suffered the injury during a Christmas Day victory over the Golden State Warriors. He partially participated during the team's shootaround Tuesday.
"He didn't do the up and down stuff," Walton said. "He did the half-court shooting and passing."
The coach added that the 34-year-old superstar has been running on his own time and is working diligently to return to the lineup.
James is in the middle of another standout season, averaging 27.3 points on 51.8 percent shooting from the field, along with 7.1 assists and 8.3 rebounds per game.
The Lakers have posted a 3-7 record in James' absence. They resume action Tuesday night against the Chicago Bulls.