ESPN, CBS Sports and The Arizona Republic, citing sources they did not name, reported the Suns have sent the two-time NBA MVP to the Lakers in exchange for draft picks.
If confirmed, the move would end a seven-year stint for Nash in Phoenix, where he had become the face of the franchise.
The Republic said the Suns will get the Lakers' 2013 and 2015 first-round picks as well as their 2013 and 2014 second-round picks in exchange for the 38-year-old Nash.
An eight-time all-star, Nash averaged 12.5 points and 10.7 assists for the Suns last season. Over his 16-year career -- including two tours with Phoenix and six years with the Dallas Mavericks -- he has averaged 14.5 points and 8.6 assists per game.
Nash surpassed Oscar Robertson for fifth place on the NBA's all-time assists list last season with his 9,897th career assist.