An Axios national political reporter said Monday he'd be "truly stunned" if President Donald Trump appointed top economic aide Gary Cohn as the next Fed chairman.

"One thing I can confirm is that Donald Trump has said to a least one official, who has no economic expertise whatsoever, that they have a better chance of being Fed chair than Gary Cohn," said Australian journalist Jonathan Swan, a well-sourced veteran of the Washington scene.

In an interview on CNBC's "Squawk Box," Swan provided a caveat: Trump is known to change his mind. "To be fair, that was a couple weeks ago when [Trump] was really angry with him. So you always need to factor in the goal-post changing," he said. "But I'd be truly stunned if Trump is seriously considering give this job to Gary Cohn."

Cohn crossed Trump in August when he criticized the president in a Financial Times interview for his response to the violence at a neo-Nazi rally in Charlottesville, Virginia. Cohn, who is Jewish, told the FT at the time the administration "must do better" in condemning neo-Nazis and white supremacists.

Speculation had swirled for months around whether Cohn, formerly the No. 2 executive at Goldman Sachs, could be a leading candidate to replace Fed Chair Janet Yellen when her term expires early next year.

But other recent reports, in addition to Swan's account, have indicated that Cohn would not be the pick and Yellen might be reappointed despite Trump's past criticism on the campaign trail that she was politically motivated to keep interest rates low to burnish the economic record of then-President Barack Obama.

Before joining Axios, which launched in January by the co-founders of Politico, Swan was national political reporter for The Hill.

— Reuters contributed to this report.