The White House declined to comment on the report.
The newspaper said the budget would include $25 billion for struggling states and provide funding increases for programs at the Energy Department, National Institutes of Health, National Science Foundation and the Census Bureau.
An administration official confirmed to Reuters that the budget would include a 6 percent increase in civilian research programs.
The budget would also provide more funds for military programs, including the Pentagon's Special Operations forces, the U.S. Army's Black Hawk and Chinook helicopters, and the F-35 Joint Strike Fighter.
Other programs and agencies would face cuts. Space agency NASA's mission to fly back to the moon would be scrapped, the paper said, and some public works projects by the Army Corps of Engineers would also lose funding.
The president has previously said he would propose a three-year spending freeze on some domestic programs that would save $250 billion by 2020.
Spending at the agencies facing cuts would be kept at $447 billion annually through 2013, the New York Times said, leading to a savings of $10 billion in the coming fiscal year.
(Reporting by Jeff Mason, editing by Anthony Boadle)