President Donald Trump should not impose a tax increase on the wealthiest Americans, media mogul and two-time GOP presidential candidate Steve Forbes told CNBC on Monday.

Axios reported last month that top White House advisor Steve Bannon is pushing for a tax increase "on the wealthiest Americans to pay for steep middle and working-class tax cuts."

"That kind of populism Ronald Reagan would have choked on," the Forbes Media chairman and CEO said on "Squawk Box." "What people want is a vibrant economy. They don't care if Bill Gates gets richer. They want to know: 'Is my paycheck going up? Are my prospects improving?'"

Axios said Trump's chief strategist told colleagues he wants the highest income tax bracket to "have a 4 in front of it" and believes this is a "potent populist idea."

Today, the top bracket is 39.6 percent for single Americans who bring home $418,401 or more annually and for married individuals filing jointly who make $470,701 or more.

Trump and Republicans in Congress have called for major tax cuts for businesses and individuals, saying that lower tax rates would drive the economy and grow jobs.

The White House and some conservative groups are targeting red-state Democrats in hopes of winning support for a tax overhaul, and Senate Democrats have offered to work with Republicans on a bipartisan package. The last time Congress passed major tax reform in the U.S. was 1986.

Forbes said Americans will get tax cuts soon but it's too late for a tax overhaul. "They botched that," he said. "Save the heavy lifting updating the code after next year's election."

Forbes unsuccessfully sought the GOP presidential nomination in 1996 and 2000. He ran on a platform for a flat tax to apply consistent rates across all brackets.

Late last month, White House budget director Mick Mulvaney said the Trump administration wants the biggest and most aggressive tax reform legislation that can pass. He said passing tax reform by the end of the year is "absolutely doable."