CNN reached out to Lockhart, who declined to comment on the news, which was first reported by Politico
The house was built in 1928 and has nine bedrooms and eight-and-a-half bathrooms. It was sold in 2014 for more than $5 million.
Obama has said
he and his family will remain in Washington home after he departs 1600 Pennsylvania Avenue in January 2017, a change from most former presidents.
"We're going to have to stay a couple of years in D.C. probably so Sasha can finish," he said in March about his youngest daughter. "Transferring someone in the middle of high school? Tough."
The Lockhart house is an 8,200-square-foot brick Tudor, and might cost $22,000 a month to rent, according to an estimate on the real estate website Zillow. It is currently valued at $7 million, according to D.C. tax assessments. It has a generous living room and dining room, a finished downstairs family room/media room, and an au-pair suite, which could be useful to the Obama family since First Lady Michelle Obama's mother has been living with the family for years. When it was last listed for sale, it was described as meticulously renovated, with gracious living rooms, exquisite finishes, a stunning oversized terrace with formal gardens, and a courtyard with enough space for 8-10 vehicles.
It is located in the upscale embassy neighborhood, next door to a former congressman and down the street from the French ambassador's residence, and around the corner from the oldest house in the city. It is about two miles from the White House, and a half-mile from the D.C. home of Hillary and Bill Clinton.
Former presidents are allotted continuing protection by the Secret Service after they leave office, so the agency will need to design and implement a security plan to protect the house and its occupants.
They would need to make an assessment of the potential dangers around the house, and possibly make a number of changes, according to former Secret Service Assistant Director Anthony Chapa.
"It's an evaluation of the whole situation -- not just the neighbors, but the street, and the park across the street," he said. For example, "We would want to talk to the neighbors," he said.
According to Chapa, alterations might include bulletproof windows and doors; reducing the underbrush across the street to provide clear lines of sight; more lighting outdoors; changes to parking rules in front of the house; and deploying electronics for monitoring the area.
"They'll have agents assigned to the residence who are here all the time, maintaining security and addressing issues," he said, and an agent would likely be posted full time at the door.
And while neighbors may face some disruption or inconvenience, Chapa said, "they've got a security apparatus coming to the neighborhood that is second to none."