But Mr Trump has said he trusts Mr Musk and is going to ask him to investigate billions of dollars of "fraud and abuse" within the US military.
Speaking to Fox News, when asked if he was serious about Canada being a 51st state Mr Trump said: "I think Canada would be much better off.
Donald Trump has repeated calls to make Canada "the 51st state" as he reiterated his support for tech billionaire Elon Musk.
Named the Department of Government Efficiency (DOGE), its aim is to find ways to sack federal workers, cut programmes and cut federal regulations.
Mr Trump also made a series of statements aboard Air Force One as he flew to the Super Bowl.