Mr Powell, a Republican and multi-millionaire, is already a member of the bank's board.
The president is set to announce his nominee for Federal Reserve chair later on Thursday.
He interviewed five candidates for the role, including current chair Janet Yellen whose term finishes in February.
Mr Powell, who has an estimated income of between $20m and $55m (£15m-£41m), has been widely tipped as the top choice for over a week.
His nomination would break with tradition, which sees presidents historically sticking with the Federal Reserve chairs appointed by their predecessors.
"I think Janet Yellen is excellent," Mr Trump told reporters during a meeting with his cabinet on Wednesday.
But asked if she was his pick, the president said: "I didn't say that."
He predicted people would be "extremely impressed" with the nominee, who will require Senate confirmation.
Mr Powell is a lawyer by training and a former partner in the Carlyle Group - one of the world's biggest investment companies.
He was appointed to the Federal Reserve board in 2012 and has voted with the majority on issues such as interest rates.