But, according to The Daily Beast, he has privately "told people close to him that he’s getting his lawyers to look into the ... matter."
The website reports that Mary, 55, signed a non-disclosure agreement after a 2001 settlement.
She and her brother, Fred Trump III, had sued their aunts and uncles in 2000 alleging misconduct in their grandfather Fred Trump Sr.'s will, which left the majority of his assets to his four living children without a fifth share intended for Fred Trump Jr., who had died in 1981.
President Trump, 74, later told The New York Times the estate fight was "very amicably" settled.
The NDA Mary signed, according to The Daily Beast, "states she is not allowed to publish anything regarding the litigation or her relationship with [Trump Jr.'s siblings] Donald, Maryanne and Robert.”
(The White House and Trump Organization did not immediately respond to a request for comment on Wednesday. Efforts to reach Mary have been unsuccessful.)
President Trump has a long history of suing or threatening to sue his opponents and it's unclear what formal response, if any, his lawyers would make.
Among the options mulled to respond to Mary, according to The Daily Beast, was a cease-and-desist letter.
Tasos Katopodis/Getty; Mary Trump/Twitter From left: President Donald Trump and Mary Trump
Simon & Schuster
Mary's publisher contends her upcoming Too Much and Never Enough will be a "revelatory, authoritative portrait of Donald J. Trump and the toxic family that made him," drawn from firsthand experience including early years in her grandparents' New York City home.
"She describes a nightmare of traumas, destructive relationships, and a tragic combination of neglect and abuse," the book's description reads. "She explains how specific events and general family patterns created the damaged man who currently occupies the Oval Office."
Mary is a clinical psychologist, according to her publisher.
"She recounts in unsparing detail everything from her uncle Donald’s place in the family spotlight and [first wife] Ivana’s penchant for regifting to her grandmother’s frequent injuries and illnesses and the appalling way Donald, Fred Trump’s favorite son, dismissed and derided him when he began to succumb to Alzheimer’s," according to the book's description.
Mary also writes of "the strange and harmful relationship between Fred Trump and his two oldest sons": her father and the president.
The White House often pushes back on unflattering memoirs from former administration officials or on unauthorized biographies of the first family.
A new biography of Melania Trump was derided by her spokeswoman as "fiction" despite being based on more than 100 interviews.
Responding to some of the details in that book, White House spokesman Judd Deere separately said: "These allegations couldn’t be further from the truth .... Hit pieces like these only serve to conjure non-existent palace-intrigue stories unworthy of the paper they’re printed on."