Steve Bannon. Chip Somodevilla/Getty Images

When the Trump administration laid out its one-page proposal for the "biggest tax cut in history" during a press conference in April, Treasury Secretary Steven Mnuchin and economic adviser Gary Cohn promised a cut for every American.

According to new reports, however, there's at least one part of the White House that wants to raise taxes for some Americans.

Jonathan Swan of the news website Axios reported late Sunday that chief strategist Steve Bannon is advocating a hike on the top tax bracket to finance a dramatic cut on taxes for middle- and lower-income Americans.

Bannon wants to get the top tax bracket, which stands at 39.5%, into the 40s, according to Axios. The top bracket applies to individuals making $418,400 or higher and couples making $470,700 or higher.

While this may not please many large Republican donors or political action groups, it is a popular message for tax reform. According to a Morning Consult/Politico poll in May, 62% of Americans believe that "upper-income people" pay too little in taxes.

The Axios report also included other insights into the Trump administration's push for tax reform, including: