The CBS newsmagazine "60 Minutes" taped an interview with Stephanie Clifford, the adult film actress known as Stormy Daniels, last week.

What's going to happen next is shrouded in mystery.

CBS producers are working on verifying claims Clifford made in the interview about her alleged affair with now-President Trump. The supposed affair dates back to 2006.

The interview could air on next Sunday's "60 Minutes." But CBS won't confirm the air date. In fact, the network won't even confirm there was an interview at all.

This is common practice -- news outlets don't like to reveal what they're working on, especially when it's a complicated or sensitive investigation.

But this is an uncommon situation. There is intense interest in what Clifford may say about Trump and the circumstances of the $130,000 payment she received in the run-up to Election Day.

The payment from Trump's personal attorney Michael Cohen, which was tied to a nondisclosure agreement, stopped Clifford from speaking to news outlets about the alleged affair before the election.

But Clifford's lawyer Michael Avenatti filed suit last week, claiming the nondisclosure agreement is invalid. With Avenatti's help, Clifford sat down for an interview last week with "60 Minutes" contributor Anderson Cooper.

Three sources confirmed to CNN that Clifford made new claims about Trump in the interview. CBS is vetting the information, the sources said.

Clifford is potentially violating the nondisclosure agreement, which means her legal battle with Trump's lawyers could be coming to a head.

BuzzFeed reported on Sunday that "lawyers associated with President Donald Trump are considering legal action to stop '60 Minutes' from airing" the interview.

But it is unclear what kind of action could actually win support from a judge -- the American legal system almost never allows such "prior restraint" of speech.

Plus, BuzzFeed noted that "Trump and his legal team often have threatened litigation without following through on those threats in the past."

Earlier this year, for example, a different Trump attorney sent threatening letters to the publisher and author of Michael Wolff's book "Fire and Fury," but the publisher went ahead with the book's release.

Cohen declined to comment to CNN on Sunday, deferring questions to his own lawyer. Larry Rosen, Cohen's lawyer, has not responded to multiple requests for comment.

CBS also declined to comment on the interview or the prospect of legal action.

"60 Minutes" already has one big interview in the works for next Sunday's program: A rare sit-down with Saudi Arabia's crown prince, Mohammed bin Salman.

The program usually has three stories per week.

-- CNN's MJ Lee contributed reporting.