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.
Avenatti said Daniels, whose real name is Stephanie Clifford, could wire transfer the money to any account by Friday.
According to the New York Times, Stephanie Clifford, who goes by Stormy Daniels professionally, would return the money so that she could speak openly about the alleged affair, Trump's attempts to keep her quiet and use and publish any "text messages, photos, and/or videos relating to the President that she may have in her possession", without legal outcome.
The White House and Cohen have denied the affair ever took place.
The NDA, which was released by Avenatti in his lawsuit filed in a California court seeking relief from the agreement, referenced Trump under the pseudonym David Dennison, while Daniels is referred to as Peggy Peterson (PP).
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The exchange would allow Clifford to speak publicly about her allegations of an affair with Trump, and according to the letter "use and publish any text messages, photos and/or videos relating to the President that she may have in her possession, all without fear of retribution and/or legal liability for damages".
"This has never been about the money", Clifford's lawyer, Michael Avenatti, told NBC News. "The designated judge from the arbitration tribunal found that Ms. Clifford had violated the agreement and enjoined her from, among other things, filing this lawsuit".
Cohen, Trump's lawyer, was given until noon (1600 GMT) Tuesday to respond. Our offer seeks to allow this to happen'.
Daniels' lawyer claims that order is not valid.
Under the terms of the deal detailed in the letter, a copy of which was obtained by The New York Times, the contract ensuring Clifford's silence would be "deemed null and void" once she returned the sum called for in her original contract. She claims in that suit to have had an "intimate" relationship with 2006 and 2007.