CNN cites two separate officials who say a man drove a vehicle to the building, saying there was a bomb inside the auto.
It was the second security-related incident near the White House on Saturday.
Metro police say the incident occurred just before 1 p.m. EST.
Trump, who was on the property, had praised the Secret Service for doing a "fantastic job" and said the suspect was "troubled".
The White House perimeter has a security fence.
US Secret Service officers stand in the cordoned off Lafayette Park after a man jumped over a bike rack in a bid to reach the fence outside the White House.
The episode comes two-and-a-half years after a series of security breaches drove then-Secret Service Director Julia Pierson to resign and thrust the agency into the political spotlight. We spend billions of dollars to secure it, ' said Dan Bongino.
The Secret Service said it had taken immediate steps to avoid further security lapses as a result of the breach.
That time Mr Trump was inside the building.
House Oversight Chairman Jason Chaffetz told CNN on Friday the intruder even rattled a door handle at the South Portico entrance to the White House. There was no mention of any harmful substances or weapons in the Secret Services' statement, but the insider alleged that Jonathan had two cans of mace with him when he was arrested. Several streets around the White House have been closed, and the situation is ongoing.
He then jumped an eight-foot White House gate near a guard post that's "not routinely staffed", according to CNN.
Secret Service agents responded after a person jumped over a pedestrian barrier outside the White House on Saturday.