Caputo, seen as a market-friendly pick, was part of the entourage that travelled with the radical libertarian, whose plans to lead the country out of an economic crisis include dollarising Argentina, erasing the fiscal deficit and closing the central bank.
"The minister of economy will be Luis Caputo," Milei told Radio La Red although his office has yet to officially confirm the nomination.
A representative for Milei did not immediately reply to a request for comment.
Caputo was already seen as frontrunner to be Milei's economy chief and last week met local and international bank officials to lay out the president-elect's proposed "shock therapy" for the embattled economy.
Milei on Tuesday met with top US advisers in Washington DC and his economic team huddled with International Monetary Fund (IMF) officials as he seeks to formulate a plan to reshape the country's foreign policy and fix its economy.
"It's key to solve (the Leliq) problem with a lot of expertise because if we make a mistake we could end up with hyperinflation," Milei said in the interview, referring to the central bank's short-term notes.
This will not be the first time for Caputo, a former Wall Street banker, as a government official.
He joined former president Mauricio Macri's administration in December 2015 with a market-friendly approach, and a few months later the country sold foreign debt for the first time since 2001 to pay a claim over defaulted notes while he was finance secretary.
Caputo also sold more than $US2.75 billion ($A4.15 billion) in a 100-year bond sale in 2017.
The economist was later appointed as central bank governor in 2018.
He resigned after three months in the hot seat in the midst of efforts to negotiate a new deal with the IMF to stem a currency crisis.
Milei, a self-proclaimed anarcho-capitalist, takes office on December 10.
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