Aside from releasing the sketch, which is being drawn up by forensic sketch artist Lois Gibson, Avenatti told CNN's Alisyn Camerota on "New Day" that there would also be a large reward for those who help identify the person.
"A composite sketch has been produced. We're going to be releasing that tomorrow, along with a significant reward," Avenatti said. "We are asking that the public come forward. We are very close to identifying this individual."
"We are going to offer a significant reward to get us over the goal line and I am confident we are going to get there," he added.
Prior to his interview, Avenatti hinted at the sketch on Sunday after he shared an image of Daniels and Gibson working together to draw up the composite.
Daniels first made mention of the threat during her much-anticipated "60 Minutes" interview on CBS.
"A guy walked up on me and said to me, ‘Leave Trump alone. Forget the story,'" Daniels told interviewer Anderson Cooper. "And then he leaned around and look at my daughter and said, ‘That's a beautiful little girl. It'd be a shame if something happened to her mom.' And then he was gone."
Though Daniels told Cooper that she never saw the man again after that, the actress said she would recognize him if she ever did see him again. Since Daniels publicly spoke about the incident, Avenatti has suggested that the threat came from someone connected to Trump or the Trump Organization.
Hours after the sharing the image on social media, Avenatti revealed that he'd filed a new motion seeking to depose Trump and Cohen over the $130,000 hush agreement arranged between Michael Cohen, Trump's personal lawyer, and Daniels prior to the 2016 presidential election.
Mirroring Avenatti's prior filing, the renewed motion requests the opportunity to question both Trump and Cohen for two hours and requests various documents related to the nondisclosure agreement. The lawyer's March 27 attempt to depose Trump and Cohen was blocked by a federal judge who ruled Thursday that the motion was "premature."
Though Trump has kept relatively mum on the issue, he broke his silence Thursday when a reporter aboard Air Force One questioned him over the payout.
"No," Trump told the reporter when asked if he knew about the payment. "You'll have to ask Michael Cohen. Michael is my attorney. You'll have to ask Michael."
Trump later noted that he did not know where Cohen got the money to pay Daniels.
Daniels is currently locked in a legal battle to void the nondisclosure agreement forcing her to keep silent about the alleged affair. The 39-year-old is arguing that the deal is invalid because 45 never signed it.