Daniels, who received $130,000 in a "hush agreement" from Donald Trump's lawyer to stay quiet about her alleged affair with the now-president, returned to the news cycle this week by announcing her plan to tell all about her relationship with the president.
Mr Avenatti gave Mr Trump's lawyer until mid-day on Tuesday to answer the offer from Ms Clifford.
I'm confident a GoFundMe campaign to raise a 130K for Daniels-I'm guessing she spent the money Cohen paid her in October-would be a success.
Cohen last month admitted to paying Daniels $130,000 through an LLC ahead of the election so she wouldnt discuss her claimed affair, which court documents say lasted from 2006 to 2007.
"Mr. Cohen and the president should take this deal and allow the American people to learn the truth", Avenatti told Fox News Monday.
The actress also seeks to "use and publish and text messages, photos and videos relating to the president that she may have in her possession, all without fear of retribution or legal liability".More news: South Korean President: summits to bring significant change
BuzzFeed also reported that attorneys associated with Trump are considering filing a legal injunction aimed at preventing CBS from airing the interview with Clifford, citing an anonymous source. It is still unclear whether or not Trump was aware of the payment, though Cohen said he was not reimbursed.
In a lawsuit filed last week, Ms Daniels alleged Mr Cohen had coerced her into signing a statement denying the relationship earlier this year. But Trump's alleged fetish for being sexually mistreated by women would contradict that carefully crafted "tough guy" image, Marshall wrote.
The POTUS was addressing the crowd at a Pennsylvania political rally on the weekend, when he spoke out Melania's role as his wife - and her duties in the White House.
Trump can hope that the prospect of a libel suit will scare CBS out of airing the interview, or he can hope that further reporting will cause 60 Minutes to conclude that Daniels is not credible and thus abandon the interview for journalistic reasons.
The offer of payment to Trump represents a shift by Avenatti, who said last week, "If she is ordered to return the money in order to invalidate the agreement, she will strongly consider doing so". Daniels and Avenatti, though, argue that it means that there is no existing agreement between Daniels and Trump, and that Daniels can speak on the subject as she pleases.