Barnes, 27, one of the top small forwards in the marketplace, will pursue a long-term deal.
Barnes and the Kings remain open to exploring a long-term deal after a successful partnership in the final few months of the 2018-19 season, league sources said.
Barnes could join what promises to be a free-agent landscape that includes 10 teams with over $20 million in salary-cap space.
Sacramento traded with Dallas for Barnes last season, with the hopes of making him a long-term focus of a franchise core that includes guards De'Aaron Fox and Buddy Hield and forwards Bogdan Bogdanovic and Marvin Bagley III.
Barnes averaged 16.4 points with the Dallas Mavericks and Kings in 2018-19, splitting the season between the two teams after the February trade.
Barnes played two-plus years with the Mavericks after signing a $94 million free-agent deal there. Barnes left the Golden State Warriors upon Kevin Durant's arrival in free agency in 2016. Barnes was part of a 2015 NBA championship team with the Warriors and won a gold medal as part of Team USA in the 2016 Rio Olympics.