Mnuchin's chief of staff, Eli Miller, flew to Palm Beach "several months ago" on the Trian Fund Management chief executive's jet, according to The Washington Post , which first reported the flight. Miller was appointed to the position in February.

The revelation, which the Treasury inspector general's office is reviewing, comes as multiple Trump Cabinet officials face questions about the ethics of using private air travel. News of the flight also came amid the Treasury's work on a tax-reform plan, which could heavily affect hedge-fund managers like Peltz.

The department gave this statement to CNBC:

"The Treasury ethics office advised Mr. Miller that he was permitted to accept a seat on a plane from a friend with whom he has a pre-existing relationship under federal ethics law."

Trian declined to comment to CNBC.

Health and Human Services Secretary Tom Price resigned last week following revelations that he took private and military jets that cost taxpayers more than $1 million in total, sometimes when cheaper commercial travel was available.

The Treasury's inspector general is already looking into Mnuchin's travel, after he and his wife took a government jet to Kentucky. He also requested to use a government plane for his honeymoon in Europe.

The inspector general's office said its review of the flight to Louisville so far shows that it was not timed to coincide with the solar eclipse in August. The watchdog is expected to complete its review this week.

Following President Donald Trump's election last year, Peltz told CNBC that Trump's tax proposals would be a boon for American companies.