The lawsuit against Keith Davidson and Cohen claims that the two attorneys colluded to discredit the adult film actress and manipulate her over her alleged affair with Trump in 2006.
It says the pair started working together in January after becoming aware of an article by In Touch magazine concerning Trump and Daniels, whose legal name is Stephanie Clifford.
"Believing this story to be detrimental to his own interests or those of his client, Mr Cohen immediately colluded with Mr Davidson in an attempt to use and manipulate Ms Clifford in a manner designed to benefit Mr Cohen and Mr Trump," according to the suit.
Specifically, the suit alleges that the two lawyers "hatched a plan" to have Daniels appear on Sean Hannity's program on Fox News in order to falsely deny her alleged affair with Trump. She ended up not appearing on the show.
The complaint, filed by Daniels' new firebrand attorney Michael Avenatti, includes copies of alleged text messages between Davidson and Cohen over a three-month period ending in March.
Cohen in one message in January refers to Davidson as "pal" and instructs him in another message to oversee any interviews or statements by Daniels.
The lawsuit also claims that Trump was aware the two lawyers were working together on his behalf.
"That said, attorney Davidson is very happy that he (Avenatti) has filed this lawsuit because he strongly believes that the filing constitutes a full and complete waiver of the attorney-client privilege," he added in a statement.
Brent Blakely, Cohen's attorney, also denounced the suit as having no merit.
"It appears to be yet another publicity stunt, and nothing more," he was quoted as saying by CNN. "We look forward to defeating the lawsuit in court."
Trump in May admitted that he had reimbursed Cohen for $130,000 in hush money paid to Daniels to stop her from going public.
Daniels is suing to be released from the hush agreement reached with Cohen, claiming it is invalid because Trump never signed it.
(Except for the headline, this story has not been edited by NDTV staff and is published from a syndicated feed.)