Trump has expressed interest in acquiring more icebreakers for maritime patrols off Canada, which could be funded through the US defense budget for next year, the report said.
Trump has serious concerns about Canada's vulnerability to US opponents in the Arctic, officials said.
"The world doesn't see Canada as a major force when it comes to defense," a senior official said.
In early October, Trump said the US had ordered 11 icebreakers from Finland, with four to be built at Finnish shipyards and the rest in the United States.
In late November, Trump said the US lags significantly behind Russia in terms of the size of its icebreaker fleet.