In the motion, filed in federal court in California on Sunday night, Avenatti also requested the production of documents on issues related to the agreement, which Daniels says is invalid.
Daniels is also seeking an accelerated jury trial to determine the validity of the agreement.
In Sunday's legal filing, Avenatti requests a Trump deposition of no more than two hours, a Cohen deposition of no more than two hours and 10 requests for production of documents directed to Trump and Cohen.
Avenatti said the questions he wants to ask include whether Trump is "David Dennison" or "DD", as mentioned in the agreement; if Trump knew about the agreement; if he "really did not know about the $ 130,000 payment"; if the payment was made with Trump's money; what was Cohen's role; and "it was Mr. Trump personally in an effort to silence the Claimant to benefit her presidential campaign by preventing voters from listening to the Claimant speak publicly."
The motion is the latest in the legal battle between Daniels, an adult film actress whose real name is Stephanie Clifford, and Cohen, Trump, and the limited liability company Cohen created to pay her to keep quiet about the supposed romance with Trump more than a decade ago.
Daniels said she was pressured to sign the document, and her legal team now says the agreement is invalid because it was never signed by Trump. Cohen has argued that it should be considered effective.