Cousins is in the final year of his contract and can become an unrestricted free agent during the offseason.
Cousins was named an All-Star starter Thursday and has now been named to the All-Star Game in each of the past four seasons.
As one half of a dynamic frontcourt duo with Anthony Davis, Cousins is averaging 25.3 points, 12.7 rebounds, 5.1 assists, 1.6 blocks and 1.6 steals per game this season.
Cousins is in the midst of his first full campaign with the Pelicans as they acquired him from the Sacramento Kings prior to last season's trade deadline.
With Cousins and Davis leading the way, the Pels are tied with the Los Angeles Clippers for seventh in the Western Conference with a record of 23-21, which gives them a half-game lead over the ninth-place Denver Nuggets.
On Wednesday, ESPN's Adrian Wojnarowski said on The Dan Le Batard Show (h/t Jake Madison of LockedOnPelicans.com) that New Orleans wants to re-sign Cousins during the offseason.
Boogie currently has the Pelicans on track to make their first playoff appearance since 2014-15.