The U.S. administration is concerned with "specific" trade deficits in specific regions of the United States, rather than looking at trade balances overall, according to a former chief economist of the International Monetary Fund.

Raghuram Rajan, speaking to CNBC on Tuesday, also called for the United States to gauge its performance beyond "narrow measures," given that the trade deficit is likely to get bigger.

The U.S. actually runs a surplus in services, said Rajan, who noted that surplus "didn't enter the equation," when President Donald Trump falsely claimed that the U.S. runs a trade deficit with Canada, as reported last week.

"President Trump said, 'No, we are running a trade deficit.' What he meant here is, we're running a manufacturing or a goods trade deficit. In fact, the U.S. is running a surplus in services," said Rajan, who was at the Credit Suisse Asian Investment Conference in Hong Kong.

"It didn't enter the equation because services go to the guys in the cities, not the constituencies that are manufacturing goods — I think that's very, very telling of what the priorities of the administration are: It's not about fixing the deficits, it's about fixing specific deficits in specific industries," said Rajan, also formerly India's central bank governor. He's now a finance professor at the University of Chicago Booth School of Business.

CNBC contacted the White House for a comment, but it did not immediately respond.