The incident is reported to have taken place during the 2018 North Korea summit in Singapore. This was the first time an American president and North Korean leader have ever met in person.
Mr Trump’s press secretary, Sarah Huckabee Sanders, described the incident in her memoir ‘Speaking for Myself’.
The book deals with Ms Sanders life including her time in the Trump White House from 2017 to 2019.
She wrote: “We made direct eye contact and Kim nodded and appeared to wink at me.
“I was stunned. I quickly looked down and continued taking notes.
“All I could think was, ‘What just happened? Surely Kim Jong-un did not just mark me!?’”
The incident took place whilst Mr Trump and Kim were discussing sports with a focus on women’s football.
Later President Trump told Ms Sanders he though the North Korean dictator was making a pass.
He commented: “Kim Jong-un hit on you.
She replied “Sir, please stop” in response to President Trump’s comments.
Mr Trump met Kim in Singapore in a bid to persuade the North Korean dictator to give up his country’s nuclear weapons stockpile.
The pair met again in Vietnam and on the Korean border the following year.
However North Korea refused to give up its nuclear weapons and talks later collapsed.
President Trump also caused controversy by praising Kim, who runs North Korea as a communist dictatorship.
During a rally in Wheeling Mr Trump said he and Kim “fell in love” and praised the North Korean letter for sending him “beautiful” letters.
Earlier this year the United States offered North Korea help fighting coronavirus but this was not taken up.
North Korea has yet to officially report any COVID-19 cases.
However, in July Kim admitted the deadly disease “could have entered” the country.
The North Korean city of Kaesong was put into lockdown in the same month for three weeks.