The consideration of the new rule comes as the president heads to Roseburg, Oregon Friday to offer his condolences to the families of the victims from last week's mass shooting at Umpqua Community College.
Mr. Obama, who has expressed mounting frustration over Congressional inaction on gun control, called last week for the partisan bickering to stop.
"Our thoughts and prayers are not enough," the president said last Thursday in a statement from the White House briefing room. "It's not enough. It does not capture the heartache and grief and anger that we should feel. And it does nothing to prevent this carnage from being inflicted someplace else in America."
The latest rule change was first considered in 2012, after a lone gunman opened fire and killed 20 schoolchildren and six adults at Sandy Hook Elementary School.
"As a country, we have been through this too many times," the president said the day of the Newtown, Connecticut shooting. "We're going to have to come together and take meaningful action to prevent more tragedies like this, regardless of the politics."
The difference the new order could make is questionable. Many gun dealer sales are already covered by the president's previous executive actions which require sellers "in the business" of dealing firearms to have a federal license and perform background checks. The new order, however, would make clear what it means to be "in the business" of selling firearms.
The president has seen increasing gun-related violence over the course of his presidency and has addressed the nation nearly a dozen times after domestic mass shootings.
Early Friday, another school shooting occurred at Northern Arizona University in Flagstaff. One person was reported killed and three wounded.
CBS News' Major Garrett contributed to this report.