It would be the first time that a major professional sports league in North America lost an entire season of competition for any reason.
Deputy commissioner Russ Granik said Thursday that the labor relations committee would make a report to the Board of Governors at next month's meeting in New York.
"If we do not have a collective bargaining agreement by that date, then David and I will have to recommend to the board that the 1998-99 season be canceled," Granik said.
There was no immediate reaction from the National Basketball Players Association. Stern is on vacation in Aspen, Colo., and union leader Billy Hunter is in Oakland, Calif., for the holidays.
No talks are scheduled in the dispute, which centers on players and owners trying to decide how to divide $2 billion in annual revenue.
"I assume that some additional negotiations will take place in advance of Jan. 7, but nothing has been scheduled at this time," Granik said.
Before Wednesday, Stern had adamantly refused to discuss a "drop dead date."
Stern told Fox Sports News on Tuesday that he talked to Hunter recently.
"I've told him we have serious disagreements," Stern said. "I'd love to sit down and negotiate. I would say we are getting pretty close" to losing the season for lack of a contract after owners locked out players.
Before this season, the NBA had never lost a single game because of labor disputes. So far, 358 games have been canceled.
On Wednesday, the shutdown reached its 158th day. The last round of bargaining took place nearly two weeks ago, and players continue to lose $50 million a week in salaries.
While baseball has had eight work stoppages since 1972, including a 232-day strike that wiped out the 1994 World Series, it has never lost an entire season. In 1918, the season ended a month early when the United States entered World War I.
The NFL and the NHL played through both World Wars and, like baseball, never lost an entire season of competition to labor strife.
In addition to salaries, some players are also losing endorsement revenue. Nike, the world's largest athletic shoe company, is exercising its option to withhold quarterly payments to most of the 230 NBA players it has under contract.
"We are doing this because the lockout is hurting fans, it's hurting the sport, and it's hurting the value of our investments in the NBA," Nike spokesman Vizhier Mooney said.
Fila USA also has stopped paying five of its 10 NBA players, but Adidas is still fulfilling its endorsement contracts.