Obama is proposing to spend $12.2 million for the 2010-2011 school year to continue the program for about 1,700 kids. The official spoke on condition of anonymity because the proposal has not been made public.
The president would like to continue the funding until all the students participating in the program graduate from high school. He would not let new students into the program, the official said.
Obama plans to release his 2010 budget proposal in detail on Thursday.
The voucher program gives scholarships to poor students in Washington so that they can attend private schools. It is the only federal voucher program in the country.
The five-year pilot program was originally set to end this year, but that date had been pushed back until June 2010.
Democrats, teachers' unions and other opponents have tried to kill the program, saying public schools can't improve if public money is being redirected to private schools. But Republicans say parents deserve a choice if their kids are in failing schools.
A spokeswoman for the city's public schools referred calls about the program to the mayor's office, which did not immediately respond to a request seeking comment.
While many urban school leaders oppose vouchers, D.C. schools Chancellor Michelle Rhee has said she is open to the program.
Although Education Secretary Arne Duncan opposes vouchers, he told The Associated Press in March that D.C. children already receiving vouchers to attend private schools should be allowed to stay there.
"I don't think it makes sense to take kids out of a school where they're happy and safe and satisfied and learning," he said.
A three-year analysis released in April by the Education Department found that D.C. students receiving vouchers made modest gains in reading but no measurable progress in math.