Curry, who has been with "Today" since 1997, replaced Meredith Vieira last June as Lauer's partner. Lauer agreed to a long-term contract this spring to stay with the show.
It's still uncertain whether Curry, who has discovered a passion for international reporting in recent years, will remain with "Today," according to a source with knowledge of the show who spoke on condition of anonymity on Wednesday because the source was not authorized to speak on the matter. The New York Times first reported the discussions about the possible change on Wednesday.
NBC News President Steve Capus and the "Today" executive producer, Jim Bell, did not immediately return requests for comment.
Savannah Guthrie, who co-hosts the show's third hour, is at the top of the list of Curry's possible replacements.
"Today" lost in the ratings this spring for the first time since 1995 after a string of 852 consecutive weeks. Since then, "Today" and ABC's "Good Morning America" have been trading weekly wins.
Keeping "Today" on top is serious business for NBC. Now four hours long, "Today" is the network's most profitable show and, with no end in sight for the network's prolonged prime-time slump, stands with Brian Williams' "Nightly News" as NBC's most successful program.
The Times reported that Curry had hired Washington lawyer Robert Barnett to represent her in talks with NBC News about her future. Barnett said he would not comment on Curry Wednesday, and Curry did not return an email seeking comment.
NBC is getting ready to take "Today" to London during the Summer Olympics in July, a high-profile period when the show will be closely watched.
Asked a week ago whether "Today" was considering any personnel changes, Bell deflected the question with a joke, saying there was no truth to the rumor that Hoda Kotb and Kathie Lee Gifford would leave as hosts of the show's fourth hour.
Bell, who is also producing NBC's Olympics broadcasts, said it would be wrong for "Today" not to undergo some self-examination with the new competition from ABC. But he also noted that ABC was helped this spring because it had a stronger prime-time lineup than NBC and some of those evening viewers stuck around for "Good Morning America."
"It feels like there's an evolution that's to take place now in the (morning) and I think, as has been the case in the past, we'll be the ones to lead the way," Bell said.
Lauer, during a CNN interview last month, said he took responsibility for his show's ratings troubles and that was one of the reasons he decided to sign another multi-million dollar contract.
"The show is not where I want it to be right now," Lauer said. "The ratings are not where I want them to be. I want to make it better and I want to reinvigorate the show in some ways that perhaps we have let up on in the past couple of years."
Curry was passed over for Vieira in 2006 when NBC executives were replacing Katie Couric on "Today." After getting the job last year, she told The Associated Press that she would not have left the show even if she had been passed over again.
"It would have been nuts abandoning the broadcast," she said. "It would have been abandoning our viewers. I love our viewers ... I have a real sense of service when it comes to this job, taking care of the viewer and helping them have information that I think they should know and want to know."