The exact date of the trip was not released but the newspaper reported it would happen in mid-March.
Trump last week lashed out at what he called California officials' "lousy management" and threatened to pull federal immigration agents out of the state.
"They're doing a lousy management job, they have the highest taxes in the nation and they don't know what's happening out there. Frankly it's a disgrace, the sanctuary city situation, the protection of these horrible criminals," Trump said.
The wall prototypes represent the signature promise of Trump's campaign: To build a "big, beautiful wall" along the U.S.-Mexico border.
He has so far been unsuccessful in his attempts to have Mexico pay for the wall, as he had promised, nor has he been able to secure $18 billion for the project from Congress, which would pay for 300 miles of new barriers and the replacement of 400 miles of existing fencing, according to The Post.