The move signals Steele's plan to reshape the party, which was trounced at the polls in 2006 and 2008.
As a black man from Maryland, a traditionally Democratic state, Steele has already brought a new face to the party.
The RNC has about 100 staff members, many of whom have been told that their last day on the job will be Feb. 15, a Republican source told Politico, which reported the story Thursday morning.
Some aides may stay on, the source said, but several senior aides who were expecting the changes voluntarily submitted their resignations soon after Steele's election last week.
President Obama's new team made a similar request at the Democratic National Committee.
Steele, a former Maryland lieutenant governor, won the chairmanship last Friday. In his first speech as chairman, he pledged to bring change in an effort to re-establish the GOP presence in the Northeast and win elections in regions across the country.
"It's time for something completely different, and we're gonna bring it to them," he said in his acceptance speech. "Get ready, baby. It's time to turn it on."