It was agreed Mr Sajudin would be paid $30,000 for the rights to the story but would be liable to pay AMI $1 million if he breached the contract.
The signed agreement does not mention the details of the story itself beyond saying: "Source shall provide AMI with information regarding Donald Trump's illegitimate child …"
"Mr Sajudin has been unable to discuss the circumstances regarding his deal with American Media Inc. and the story that he sold to them, due to a significant financial penalty," Mr Held told CNN.
"Just recently, AMI released Mr Sajudin from the terms of his agreement and he is now able to speak about his personal experience with them, as well as his story, which is now known to be one of the 'catch and kill' pieces. Mr Sajudin hopes the truth will come out in the very near future."
The existence of this safe at the National Enquirer made headlines worldwide this week after several media outlets reported that federal prosecutors have granted immunity to Mr Pecker, potentially laying bare his efforts to protect his longtime friend Mr Trump.
It is reported to contain documents on hush-money payments and other damaging stories the National Enquirer, under the leadership of Mr Pecker, killed as part of its cozy relationship with Donald Trump leading up to 2016 presidential election.
Several people familiar with the Enquirer's parent, AMI, who spoke to the Associated Press on condition of anonymity because they signed nondisclosure agreements, said the safe was a great source of power for Mr Pecker.
The details of the safe also come as Mr Trump's former lawyer Michael Cohen pleaded guilty this week to campaign finance violations alleging he, Mr Trump and the tabloid were involved in buying the silence of a porn actress and a Playboy model who alleged affairs.
The Trump records are reportedly stored alongside similar documents pertaining to other celebrities' catch-and-kill deals that the Enquirer has no intention of publishing to keep them out of the news.