The people spoke to The Associated Press on condition of anonymity on Saturday because the free-agent contract, which cannot officially be signed until July 9, has not been announced.
The Pelicans first signed the 6-foot-8 Cunningham as a free agent last December. He played in 66 regular season games, starting 27, and averaged 5.2 points and 3.9 rebounds in 25 minutes.
The 28-year-old Cunningham was relied upon mostly for his defense. His contract includes a third-year player option. His return gives the Pelicans nearly all of their regulars back for next season except guard Norris Cole, who remains a restricted free agent.
AP Basketball Writer Jon Krawczynski in Minneapolis contributed to this report