Nance, who the Pelicans acquired from the Portland Trail Blazers on Tuesday in the deal that also sent CJ McCollum and Tony Snell to New Orleans, has not played since Jan. 5. He has been listed as out during that time with right knee soreness.
If Nance comes back in six weeks, he should be available for the final few weeks of the regular season.
The Pelicans are 22-32 and have a 1½-game lead on the Trail Blazers for the 10th and final spot in the Western Conference play-in tournament.
Nance is averaging 6.9 points and 5.6 rebounds in 37 games this season.
McCollum and Snell arrived in New Orleans on Wednesday and are expected to make their season debuts for the Pelicans on Thursday night against the Miami Heat.