
API VIA GETTY IMAGES Image caption, Donald Trump and Kim Jong-un, seen here in 2019, failed to reach a deal to denuclearise the Korean peninsula
Journalist Maggie Haberman said Mr Kim was the only foreign leader Mr Trump had said he remained in touch with.
But, she added, the claims could not be verified and might not be true.
In 2018, Mr Trump famously said he and Mr Kim “fell in love” after exchanging letters. But they failed to seal a deal to denuclearise the Korean peninsula.
Communications between a former US president and Mr Kim would be highly unusual, given North Korea’s international isolation because of its nuclear and missile programme.
“As we know, [Mr Trump] had a fixation on this relationship,” Haberman, a New York Times journalist, told CNN. The revelation is in her upcoming book on Mr Trump, The Confidence Man.
- ANALYSIS: What does Kim Jong-un want?
- CONTEXT: North Korea’s missile and nuclear programme
Correspondences from Mr Kim were among the documents in 15 boxes of papers retrieved from Mr Trump last month by the National Archives, the government agency that manages the preservation of presidential record.
The documents should have been turned over to the agency when Mr Trump left the White House but, instead, were taken to his residence in Florida.
The National Archives asked the Department of Justice to examine Mr Trump’s handling of White House records, according to the Washington Post. A justice department spokesman did not comment.
Separately, a committee at the House of Representatives said it had opened an investigation.
Staff, she said, would then find “wads of clumped up, wet printed paper… either notes or some other piece of paper that they believe he had thrown down the toilet”.
Mr Trump denied the claim as “categorically untrue”.