"Rather, the Agreement and the $130,000 payment made pursuant to the Agreement, was for the "purpose of influencing" the 2016 presidential election by silencing Plaintiff from speaking openly and publicly about Mr. Trump just weeks before the 2016 election", he wrote in a 31-page motion.
If she is successful, it would be the first deposition of a sitting president since Bill Clinton in 1998 had to answer questions about his conduct with women.
Stormy Daniels' attorney Michael Avenatti has filed a motion in federal court seeking to depose President Donald Trump and his lawyer Michael Cohen to ask about a $130,000 payout before the 2016 election.
At the time, Trump was married to his current wife, Melania, who had recently given birth to their son, Barron.
As for Cohen's efforts that led to the payment to Daniels in 2016, Schwartz said in the interview that Trump "was not aware about any of it".
Mr Trump's lawyer's lawyer, David Schwartz, dismissed the motion as "a reckless use of the legal system in order to continue to inflate Michael Avenatti's deflated ego and keep himself relevant".
The persistent focus on Ms Daniels is a troubling distraction for a White House already struggling with an exodus of top staffers, a floundering agenda and the looming threat from the Russian Federation investigation.
Avenatti wants to question each for "no more than two hours".
Mr Trump's legal team is in continued negotiations with special counsel Robert Mueller over the scope and terms of an interview with the President.
But her lawyer argues that the agreement is invalid because Trump failed to sign the document.
On whether Daniels would accept a settlement, Avenatti said: "We would never consider any settlement that did not include everyone coming 100% clean with the American people".
Stormy Daniels appears with Anderson Cooper on "60 Minutes".
"Those are, I think, the key political issues here, and filing this lawsuit gives Avenatti another opportunity perhaps to get Cohen and perhaps Trump under oath", he said.
In the "60 Minutes" interview, Ms Clifford said she signed the denial because she believed Mr Cohen would make her "life hell in many different ways".
The lawyer said his aim was to establish if the president had consented to the agreement.
A hearing in Los Angeles is set for 30 April. I mean, we're relying on U.S. Supreme Court precedent and a whole line of cases in the Ninth Circuit Court of Appeals. The appeal was still pending when Clinton agreed to pay $850,000 to settle the case.
Attorneys for a former contestant on one of Mr Trump's "Apprentice" reality TV shows say they want to depose the President as part of a defamation suit.