ESPN's Adrian Wojnarowski reported as much on the Monday edition of his The Woj Pod podcast.
Los Angeles was previously linked to Williams, who was a Philadelphia 76ers assistant coach this season. In April, Wojnarowski noted the Suns were "planning to target" him even though the Purple and Gold were "planning a second interview with Williams soon."
While Wojnarowski said on the podcast the Lakers seemed ready to hire Williams, Brad Turner of the Los Angeles Times reported on Friday that Tyronn Lue was "always" the team's top choice.
Wojnarowski and colleague Ramona Shelburne reported on Friday the Lakers were "proceeding toward an offer" for the former Cleveland Cavaliers head coach and "have no plans to introduce new candidates."
Lue has plenty of experience with LeBron James from their time in Cleveland and reached three straight NBA Finals, winning one.
As for Williams, he was the head coach of the New Orleans Hornets/Pelicans for five seasons from the 2010-11 campaign through the 2014-15 one and finished with a 173-221 record and two playoff appearances. He lost in the first round both times.
He takes over a Phoenix team that finished with the worst record in the Western Conference this season at 19-63 but has young pieces in place in Devin Booker and Deandre Ayton, as well as a 2019 draft pick that has a 14 percent chance at becoming the No. 1 overall selection.