A source close to the actress said that it included new details of her relationship with Mr Trump, which she claims began in 2006, shortly after his wife, Melania, gave birth to their son, Barron.
It also seeks to stop Trump and Cohen from trying to block her upcoming appearance on '60 Minutes'.
In an apparent effort to link him directly to the deal, Daniels offered to "pay $130,000.00 to President Trump" by Friday.
"On information and belief, EC was created by Mr. Cohen with Mr. Trump's knowledge for one objective - to hide the true source of funds to be used to pay Ms. Clifford, thus further insulating Mr. Trump from later discovery and scrutiny".
If Mr Trump's lawyers accept the offer, Ms Clifford will be able to talk about both the relationship - which the President and his lawyer deny - and the alleged attempts to buy her silence.
Nun Involved in Legal Battle With Katy Perry Dies in Court
Katy Perry , meanwhile, is busily promoting ABC's reboot of the singing competition American Idol , on which she is a judge. A few hours before her death Sister Catherine spoke to Fox 7 News in which she urged Katy to fall back on the legal battle.
Cohen, who has admitted to facilitating the $130,000 payment to keep Clifford quiet, denies that the negotiations or the payment were made on behalf of the Trump Organization or the Trump campaign.
Avenatti said last week that Daniels "believes it's important that the public learn the truth about what happened". But her spokeswoman said last month that Daniels planned to "tell her story", prompting Trump's lawyers to obtain a temporary restraining order from a private arbitrator.
As Stormy Daniels plied her trade at one or more Florida strip clubs over the weekend, she continued her assault on the American media - and, some might say - its mores.
The reason Cohen is twisting himself into such absurd logical knots is because if he acted to buy Daniels' silence and boost his client's shot at winning the White House, the payment is nearly certainly an unlawful, unreported campaign contribution.
A recently taped interview she gave to "60 Minutes" would also be protected from any legal action by Trump or the LLC used to pay the adult film star.
Good-government groups have questioned the payment Cohen made, suggesting it may have violated election rules - especially after news he arranged the payment with his Trump Organization email address.