Trump suggested last month at a rally in Arizona that he would be willing to shut down the government if Congress sent him a funding bill that didn't include money for a wall between the U.S.-Mexico border.
"If we have to close down our government, we're building that wall," Trump said.
Two days after Trump's rally, the White House told Congress the money did not need to be in a "continuing resolution" to fund the government from October until sometime in December, The Washington Post reported, citing a senior GOP congressional aide.
However, Trump wants border wall funding to be included in a December budget bill, the Washington Post reported, citing GOP congressional aides.
Government funding expires at the end of September. Congress is expected to pass a short-term funding bill while it crafts a long-term one.