She has written that President Trump developed "twisted behaviours" and saw "cheating as a way of life," according to The New York Times.
Ms Trump alleged that the future US leader cheated on the SAT pre-collegiate exam, helping him get into the University of Pennsylvania's prestigious Wharton business school, the newspaper reported.
She said her uncle paid someone else to take the test but The Times doesn't explain how she knew.
The 240-page book, out July 14, said Mr Trump is a product of his "sociopath" father Fred Trump, The Washington Post reported.
Mary, a clinical psychologist, said her uncle failed to develop human emotion because his father created an abusive and traumatic home life.
She said that for the future US leader, "lying was primarily a mode of self-aggrandisement meant to convince other people he was better than he actually was," the Post said.
The memoir has been billed as the first unflattering portrayal of Mr Trump by a family insider.
The president's younger brother Robert Trump went to court to try to block publication, arguing that Mary was violating a non-disclosure agreement signed in 2001 after the settlement of her grandfather's estate.
Last week, a New York appeals judge ruled that Simon & Schuster is allowed to release the memoir, saying it was "not a party to the agreement."
On Tuesday, White House spokeswoman Kayleigh McEnany described it as "a book of falsehoods," even though she admitted she hadn't seen it.
"It's ridiculous, absurd allegations that have absolute no bearing in truth," Ms McEnany told reporters.
Mary is the son of Fred Trump Jr, Trump's older brother, who died in 1981 from complications related to alcoholism.
Fred Trump Sr died in 1999.
She has written that her uncle meets all the clinical criteria for being a narcissist, according to The New York Times.
"Donald's pathologies are so complex and his behaviours so often inexplicable that coming up with an accurate and comprehensive diagnosis would require a full battery of psychological and neurophysical tests that he'll never sit for," she writes.
The memoir will also reveal that Mary was the crucial source for explosive New York Times reporting on Mr Trump's finances, which suggested the billionaire paid little in tax for decades, according to The Daily Beast.
In the book, she will quote the president's sister Maryanne Trump Barry as "saying he's a clown - this will never happen," after Mr Trump announced he was running for president.
It is set to be the latest bombshell book to dish dirt on President Trump after former aide John Bolton's tome, which describes the Republican leader as corrupt and incompetent, hit shelves last month.