Turner, a guard who has been selected to five straight Pro Bowls, is signed through the 2021 season and is scheduled to earn base salaries of $8.5 million and $11 million the next two seasons, respectively.
Turner, however, wants a new deal, sources told ESPN's Adam Schefter.
The trade cannot be made official until 4 p.m. on March 18, the start of the NFL's new league year.
Okung, a two-time Pro Bowl selection at left tackle, has one year left on his contract and is scheduled to be paid a base salary of $13 million.
Turner, who turns 26 on June 14, has started 80 of the 84 games he has appeared in for the Panthers since Carolina selected him in the third round of the 2014 draft.
Okung, who turned 32 in October, was the sixth overall pick by the Seattle Seahawks in the 2010 draft. He joined the Chargers as a free agent in the 2017 offseason and has spent the past three seasons with the team.
Okung began last season on the reserve/non-football illness list because of a pulmonary embolism caused by blood clots during the offseason. He was activated in late October. He has started all 124 games of his NFL career.
The move will reunite Okung with his former offensive line coach with the Chargers, Pat Meyer.