The Lakers parted ways with head coach Byron Scott on Sunday after a franchise-worst 17-65 season.
Walton, 36, has a history with the Lakers, having been on two NBA championship teams in his nine seasons as a player in Los Angeles.
This season, Walton stepped in as the Warriors' interim coach and guided the team to a 39-4 record while head coach Steve Kerr recovered from back surgery. The Warriors won each of their first 24 games, an NBA record to open a season, and they wound up with a 73-9 mark, the best in league history.
All of Walton's wins were credited to Kerr, per NBA rules.
Walton tied for eighth in NBA Coach of the Year voting, which was won by Kerr.
Kerr confirmed Wednesday that Lakers general manager Mitch Kupchak asked if he could talk to Walton. The meeting could occur soon if the Warriors close out their first-round Western Conference playoff series against the Houston Rockets on Wednesday night. Golden State holds a 3-1 series advantage in the best-of-seven series.
The New York Daily News recently reported that Walton turned down an opportunity to speak with the New York Knicks about their head-coaching job.
Golden State general manager Bob Myers said last week on the team's TV pregame show, "Luke is gonna be a head coach someday, but he's gonna be deliberate about how he goes about it, which is smart. He's got good options, I think he'll continue to have good options. He's in a good place."
Another assistant coach from the Warriors' 2014-15 championship team, Alvin Gentry, left the team to become the head coach of the New Orleans Pelicans before the 2015-16 season.