It's not the first time Williams will have been approached by the Lakers. He was not interested in coaching them in 2004 after Phil Jackson's first tour ended.
At the time, Williams was with North Carolina only one season after leaving Kansas. The Lakers eventually hired Rudy Tomjanovich, who resigned halfway through the 2004-05 season.
There are other Lakers possibilities for a file that will get only longer: George Karl, Jeff Van Gundy, Kurt Rambis, Byron Scott, John Calipari and Kevin Ollie. The Lakers are considering an interview with Tom Thibodeau but need permission from the Chicago Bulls to talk to him.
There is no clear favorite to replace Mike D'Antoni, who resigned last week after going 67-87 in almost two seasons. He had one more guaranteed year and $4 million on his contract. He received an unspecified amount from the team as part of his resignation.
The Lakers will not have a coach in place before the May 20 draft lottery. They expect to have one hired by the June 26 draft.
Williams, 63, coached North Carolina to NCAA championships in 2005 and 2009. The Tar Heels have been bounced in the third round of the tournament the last two years.
Lakers General Manager Mitch Kupchak played at North Carolina in the 1970s. He has remained close to the program through the years.
The Lakers are coming off their worst season since moving to Los Angeles in 1960, finishing 27-55, 22 games out of a playoff spot.
They currently have the sixth spot in the draft and could move as high as the top overall pick or as low as ninth at the lottery. There is a 6.3% chance they will get the No. 1 pick.