"I'm going to tell him very soon, like maybe in 24 hours, to go check the Department of Education. ... Then I'm going to go, go to the military. Let's check the military," Trump said in a Super Bowl interview with Fox News, an excerpt of which was aired on Sunday morning.
"We're going to find billions, hundreds of billions of dollars of fraud and abuse," Trump said of the largest federal department.
The Pentagon's budget is approaching $US1 ($A1.6) trillion per year.
In December, then-President Joe Biden signed a bill authorising $US895 billion ($A1.4 trillion) in defence spending for the fiscal year ending September 30.
Musk, who the White House says is a special government employee, has been tasked by Trump to lead an effort to slash the size of the US federal workforce.
As part of that initiative, Musk aides have sought access to confidential information in computer systems at various government agencies.
Critics say the efforts are likely illegal, risk exposing classified information and in practice are gutting entire agencies without congressional approval.
National Security Adviser Mike Waltz suggested in a separate interview on Sunday that the Pentagon's shipbuilding processes could be an area of particular interest for Musk's Department of Government Efficiency.
"There is plenty to look into in shipbuilding, which is an absolute mess," Waltz said in an interview on NBC.
Leaders from across the political spectrum have long criticised waste and inefficiency at the Pentagon.
But Democrats and unions say Musk' Department of Government Efficiency lacks the expertise to restructure the Pentagon, and their efforts risk exposing classified programs.
Musk's companies also hold major contracts with the Pentagon, which has raised significant conflict of interest concerns.
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