Smith and the Lakers have been discussing a deal since starting guard Avery Bradley opted out of the season restart last week, sources said.
Smith and the Lakers were working through the final details of a contract on Monday in Los Angeles, and there are believed to be no hurdles to a finalized deal, sources said.
Smith, 34, hasn't played an NBA game since November 2018 with the Cleveland Cavaliers.
Smith worked out for the Lakers in February before the team signed guard Dion Waiters. Guard Alex Caruso and Kentavious Caldwell-Pope will largely carry the burden after Bradley's departure, with Waiters expected to provide further depth in the backcourt. Rajon Rondo is another veteran guard on the Lakers' bench.
Smith has played 15 NBA seasons since New Orleans drafted him in 2004 out of St. Benedict's Prep in New Jersey. He also has made stops in Denver and New York. He won an NBA title with LeBron James and the Cavaliers in 2016 and won the NBA's Sixth Man Award in 2013 with the Knicks.
The NBA has a transaction window through July 1 that allows teams to sign free agents prior to traveling to Orlando to restart the season.