"I've told my folks that's the man and he's doing some pre-checking now and I would imagine he'd be in great shape", CNN quoted Trump as saying.
"I think what you have here is a philosophy that strong growth is not inflationary, especially when it comes from the supply side of the economy which is where it coming, as you look at the jobs and the hours worked and the business investment", said Kudlow, who served as the Trump campaign's senior economic adviser.
'I personally think the Fed should drop rates.
The U.S. president also suggested that the central bank pursue an unconventional monetary policy called "quantitative easing" that was used to nurse the economy back after the global financial crisis.
The renewal of quantitative easing, Trump said, should be in addition to interest rate cuts - a likely worrying thought, at this point, for Fed officials who describe such a combination of tactics as only appropriate in a dire downturn.
The Federal Reserve raised interest rates four times a year ago, but has since signaled a pause.
Trump's choices were seen as escalating an effort by the White House to exert political pressure on the central bank.
The president said those were unnecessary because there is "very little, if any inflation".
But the White House declared repeatedly that Trump does not plan to remove Powell as Fed chairman. None said they now back a rate cut and some have said rate hikes may eventually be necessary.
Trump has repeatedly criticized the Fed's rate increases past year, and has reportedly even discussed firing Fed Chairman Jerome Powell months ago. The Fed's policy rate is now between 2.25 and 2.5 percent.