Larry Kudlow is the leading contender to head President Trump's National Economic Council, one of Mr. Kudlow's colleagues at CNBC reported Monday.
"If he was offered it, he would take it," said CNBC's Jim Cramer.
The president is seeking to replace Gary Cohn, who announced his resignation last week after failing to stop Mr. Trump from imposing tariffs on steel and aluminum.
Later on Monday, CNN reported, citing "a source familiar with his conversations," that Mr. Trump had told people he'd decided on Mr. Kudlow.
Mr. Trump also reportedly is "seriously considering" Chris Liddell, former chief financial officer for General Motors and Microsoft, for the White House post.
Mr. Kudlow, a free-trade advocate, has declined to comment. A senior contributor on CNBC, Mr. Kudlow worked on economic policy in the Reagan administration and started his career at the Federal Reserve.