It was not clear if such documents were recovered at Trump's Mar-a-Lago resort in Palm Beach, the Post said.
Reuters could not immediately confirm the report.
The US Justice Department asked a judge on Thursday to make public the warrant that authorised the FBI search, after Trump portrayed it as political retribution.
The request means the public could soon learn more about what investigators were looking for during the unprecedented search of a former president's home.
The move was part of an investigation into whether Trump illegally removed records from the White House as he left office in January 2021, some of which the Justice Department believes are classified.
Attorney-General Merrick Garland, the country's top law enforcement officer and an appointee of Democratic President Joe Biden, told a news conference he personally approved the search.
The Justice Department also seeks to make public a redacted receipt of the items seized.
"The department does not take such a decision lightly. Where possible, it is standard practice to seek less intrusive means as an alternative to a search, and to narrowly scope any search that is undertaken," Garland said.
His decision to publicly confirm the search was highly unusual. US law enforcement officials typically do not discuss ongoing investigations. In this case, Trump announced the search in a Monday night statement.
Garland said the Justice Department made the request to make public the warrant "in light of the former president's public confirmation of the search, the surrounding circumstances and the substantial public interest".
A source familiar with the matter said the FBI retrieved about 10 boxes during the search. Trump was not in Florida at the time.
The government has until 3pm eastern time (5am Saturday AEST) on Friday to let the court know whether Trump's attorneys will object to unsealing the warrant.
While seeking to unseal the warrant, the Justice Department has not asked the judge to unseal the sworn statement in support of the warrant, the contents of which could potentially include classified information.
Two of Trump's attorneys, Evan Corcoran and John Rowley, did not respond to a request for comment.
"My attorneys and representatives were cooperating fully, and very good relationships had been established. The government could have had whatever they wanted, if we had it," Trump said in a statement on his Truth social network.
The search marked a significant escalation in one of the many federal and state probes Trump is facing from his time in office and in private business, including a separate probe by the Justice Department into a failed bid by Trump's allies to overturn the 2020 presidential election by submitting fake slates of electors.
The investigation into Trump's removal of records started earlier this year, after the National Archives made a referral to the department.
Former archivist David Ferriero has previously said Trump returned 15 boxes to the government in January 2022. The archives later discovered some of the items were "marked as classified national security information".
A couple of months prior to the search, FBI agents visited Trump's property to investigate boxes in a locked storage room, according to a person familiar with the visit.
The agents and Corcoran spent a day reviewing materials, the source said. A second source who had been briefed on the matter told Reuters the Justice Department also has surveillance footage from Mar-a-Lago.
Garland's Justice Department has faced fierce criticism and online threats since Monday's search.
Trump supporters and some of his fellow Republicans in Washington accuse Democrats of weaponising the federal bureaucracy to target Trump.
In Cincinnati, Ohio, on Thursday, an armed man suspected of trying to breach the FBI building died following an exchange of gunfire with law enforcement officers.
Garland condemned the threats and attacks against the FBI and Justice Department.
"I will not stand by silently when their integrity is unfairly attacked," he said.
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