An auction firm was accepting sealed bids through 4 p.m. (2100 GMT) on Tuesday for the five-bedroom, Tudor-style home in the borough of Queens where Trump lived until age 4.
The winner of the auction would not immediately be known because the seller plans to consider the bids for as long as a few days, Misha Haghani, a principal at Paramount Realty USA, told Reuters in an email.
Trump, whose official residence will be the White House once he is sworn in as president on Friday, has said that he would like to own his old home.
Shown a photograph of it in September while on "The Tonight Show," Trump told host Jimmy Fallon: "Oh, thats sad to look at that. I want to buy it. I want to buy it."
Representatives for Trump could not immediately be reached on Tuesday.
Paramount Realty USA markets the property as Trumps childhood home and as a chance to own a piece of history. Built around 1940 by Trumps father, the real estate magnate Fred Trump, the house has a five-car driveway, a fireplace, a sun room and a paneled study.
Real estate investor Michael Davis purchased the house in December for $1.39 million, according to property records. He did so sight-unseen, without even driving by the house, the New York Post reported.
Haghani declined to speculate on a possible winning price.
Offers needed to be accompanied by a deposit of 10 percent.