President-elect Trump told reporters on Sunday that he would be moving into the White House after his January 20 inauguration.
When asked if his wife Melania and her son Barron would join him, Mr Trump said "after he’s finished with school”.
The parents are wary of pulling their son out of school now, team communications director Jason Miller told reporters.
"There's obviously sensitivity to pulling their 10-year-old out of school in the middle of the school year. A more formal statement will be coming in the future," Mr Miller said.
He was responding to a New York Post report that Melania Trump, 46, and her son will keep living in Trump Tower at least until the end of the school year so the boy can continue attending his private school in Manhattan's Upper West Side.
The Post has cited a source close to the issue, who claimed the presidential campaign "has been difficult for Barron, and she (Melania) is really hoping to keep disruption to a minimum".
“Melania is extremely close to Barron, and they have become closer during the campaign,” the unnamed source added.
US presidents have lived in and worked at the White House since John Adams took up residence there in 1800.
