The effort could face opposition from Republicans, some of whom are reportedly worried about increasing the middle class's tax burden so soon after cutting taxes, their only big legislative achievement under Trump.
The current federal levy is 18.4 cents a gallon on retail gasoline and 24.4 cents a gallon for diesel. The increase floated by the president would presumably put the gasoline tax at 43.4 cents and diesel tax at just under 50 cents.
Trump endorsed raising the gasoline tax by a quarter at a White House meeting with members of his administration and Congress, two sources told Axios.
The president repeatedly raised the prospect of a 25-cent hike for both the diesel and gasoline tax, said Sen. Tom Carper, a Democrat from Delaware who attended the meeting and has advocated for gradually increasing the levy.
"While there are a number of issues on which President Trump and I disagree, today, we agreed that things worth having are worth paying for, and the president even offered to help provide the leadership necessary so that we could do something that has proven difficult in the past," Carper said in a statement.
The White House said it would not comment on Trump's discussions in closed door meetings.
The president has communicated to staff that he is open to raising the gas tax for weeks, ever since the U.S. Chamber of Commerce proposed it, CNBC can confirm.
The federal government has not raised the gas tax since 1993. Funds raised through the charge pay for road construction and investments in mass transportation through the Highway Trust Fund.
In the roughly 25 years since the last hike, inflation has whittled down the buying power of dollars raised through the tax. Vehicles on the road have also become more fuel efficient, further diminishing the levy's ability to fund highway repairs.
The issue has been on the table at least since May, when Trump suggested he might support raising the federal fuel levy. The White House tamped down reports of his support, but top economic adviser Gary Cohn later told lawmakers would get a chance to debate a hike during infrastructure negotiations.
Earlier this month, Cohn revisited the idea in a meeting with Republicans, where some GOP lawmakers supported the idea, while others raised concerns, Axios reported.
The opponents include Senate Majority Whip John Cornyn, who expressed his opposition in a private donor retreat hosted by billionaire industrialists Charles and David Koch.
On Monday, nearly 30 conservative groups opposed raising the gas tax in a letter to lawmakers.
"Raising the gas tax is a bad idea," the signatories wrote. "It will make the burden of government on families and businesses heavier. A higher gas tax means higher prices not just on gas, but on goods and services throughout the economy."
— CNBC's Kayla Tausche, Ylan Mui and John Schoen contributed to this report.