Trump claimed he was unaware of Cohen's payment to Daniels, whose legal name is Stephanie Clifford, until his new lawyer Rudy Giuliani revealed earlier this month that the president had reimbursed Cohen.
Daniels has alleged she had a sexual encounter with Trump in 2006, a claim he denies.
Trump submitted his financial disclosure form Wednesday, which showed he made a payment to Cohen between $100,001 and $250,000 in 2017.
The FBI raided the offices of Cohen last month, a move that Trump angrily denounced as a "disgrace" and "whole new level of unfairness".
Michael Cohen had earlier said he gave up on the project in January 2016 after determining it "was not feasible for a variety of business reasons". "I mean, there were very few people who knew the people that were being placed in a lot of jobs".
"It is good that in the face of overwhelming evidence and public pressure, the president came clean about this liability on this year's form", said CREW's Noah Bookbinder. We've recently learned Cohen was subsequently reimbursed by Trump.
That letter was written in response to a complaint from a watchdog organization, Citizens for Responsibility and Ethics in Washington, which said that Trump should have reported the payments to Cohen in last year's disclosures.
Cohen claimed he had worked with Russian-born developer named Felix Sater who has worked on a multitude of projects for the Trump Organization - including hotels in Florida and NY.
Ethics disclosures are an annual requirement for senior federal officials and are overseen by the ethics office, a government office that provides oversight of an executive branch program to prevent and resolve conflicts of interest.
The letter constitutes a referral by the ethics office of a possible false financial filing.
In April, Mr Trump said he was unaware Mr Cohen had paid Ms Daniels just before the 2016 election. Last month, his home, office and hotel room were raided by the Federal Bureau of Investigation, with records of the payment to Daniels among the materials seized.
However, the contract could not immediately be terminated and Novartis had to wait until the full $1.2 million had been paid to Cohen's company.
"OGE has concluded that the information related to the payment made by Mr. Cohen is required to be reported and that the information provided meets the disclosure requirement for a reportable liability", the agency said.
US President Donald Trump officially admitted on Thursday for the first time that he repaid his former personal lawyer up to $250,000 (€210,000), but did not explicitly say what the reimbursement was for.