The Washington Post reported that when the bill comes up for consideration it will be the first time that a D.C. voting rights proposal has been heard in more than three decades.
The newspaper said debate on the proposal is expected to be lively.
The Post reported that a similar bill was introduced three years ago but failed to muster the procedural votes needed to move forward. This session's proposal was co-sponsored by President Barack Obama when he was the junior senator from Illinois.
The bill would permanently adds two seats to the 435-member House. One would go to the Democratic-leaning District of Columbia, and the other would be assigned to Republican-leaning Utah through 2012.
Del. Eleanor Holmes Norton, the Democrat who currently represents the district as a non-voting delegate, said she is pleased the proposal is moving forward.
"I could not be more pleased that the House and Senate are moving at the same time on our D.C. House Voting Rights bill," Norton said. "The House went first last time, but this time it looks like a race to the finish and the Senate is ahead by a lap."