The White House has identified other funding sources for the project, says spokeswoman Sarah Sanders.
Mr Trump is seeking $5bn (£3.9bn) from Congress to start work on the wall.
Several federal agencies will shut down on Friday if Congress and the president fail to reach agreement on funding.
It was not immediately clear what Mrs Sanders was referring to when she mentioned potential alternative sources of funding for the wall.
During Tuesday's White House briefing, the White House spokeswoman told reporters Mr Trump had "asked every [federal] agency to look and see if they have money that can be used for that purpose".
But Democratic Senate leader Chuck Schumer said the president does not have the ability to move funds around to pay for his wall without congressional approval.
"And they're not getting it for the wall," he added.
Top House Democrat Nancy Pelosi told reporters on Tuesday that building a wall would be "a waste of money."
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