Trump is expected to unveil on Monday a fiscal 2019 budget plan that will be based on rosy assumptions including economic growth of 3.2 percent next year, a White House official said.
That level is well above the 2.5 percent growth achieved in 2017 and the 2.5 to 2.7 percent range of economists' forecasts for this year.
The White House's plan also anticipates that the strong growth will go on for years, the official said, with 3 percent growth in 2021, only tapering to 2.8 percent in 2026.
The growth assumptions in Trump's budget were first reported by the Wall Street Journal.
The Trump budget also assumes low interest rates, with the benchmark 10-year Treasury yield averaging 2.6 percent this year.
But the 10-year yield closed at 2.86 percent on Friday, and the Federal Reserve is expected to hike rates three times this year.
Such optimistic assumptions would make deficits look smaller in Trump's budget plan after Republicans in December approved massive tax cuts expected to add about $1.5 trillion in new debt over a decade.
Republicans contend the tax cuts will fuel a spike in economic growth.
The White House also will amend the budget plan to take into account the higher spending levels in the budget deal passed just before dawn on Friday, a senior official in the Office of Management and Budget said.
Friday's spending measure, which ended an hours-long partial government shutdown, was approved by a wide margin in the Senate and survived a rebellion from conservative Republicans in the House of Representatives who objected to non-military spending increases.
It was the second shutdown this year under the Republican-controlled Congress and Trump, who played little role in attempts by party leaders this week to end months of fiscal squabbling.
In a Twitter post that acknowledged the misgivings of fiscal conservatives, the Republican president said after signing the measure, "Without more Republicans in Congress, we were forced to increase spending on things we do not like or want in order to finally, after many years of depletion, take care of our Military" with additional funding.