The thinking within the Trump transition team is that the DNI often gets in the way of the 16 intelligence agencies it represents, which includes the CIA, the sources told CNN.
Trump has been a harsh critic of US intelligence agencies. He has been skeptical of the US intelligence community saying Russia was behind the hacking meant to influence the outcome of the 2016 election.
The possible move was first reported by The Wall Street Journal
Trump is also considering expanding the CIA's human spying capabilities but wants an assessment once new intelligence leadership is in place, according to sources close to the transition. There has been building criticism among conservatives that the CIA under President Barack Obama has been too reliant on electronic spying and the NSA's signals intelligence.
Trump's incoming press secretary called reports that Trump would restructure US intelligence agencies "100% false" on Thursday.
"All transition activities are for information gathering purposes and all discussions are tentative," Sean Spicer told reporters on a press call. "The President-elect's top priority will be to ensure the safety of the American people and the security of the nation and he is committed to finding the best and most effective way to do it. But I want to reiterate, there is no truth to this idea of restructuring the intelligence community infrastructure, it is 100% false."
Trump seemingly taunted the US intelligence agencies who are supposed to brief him on alleged Russian hacking via Twitter on Tuesday.
He suggested that intelligence officials postponed an "'intelligence' briefing on so-called 'Russian hacking'" that they were set to deliver to him this week because they might need more time "to build a case." He called the alleged delay "very strange."
US intelligence officials disputed Trump's tweet, saying the meeting was not set to take place until later in the week.
Rep. Adam Schiff, the top Democrat on the House Intelligence Committee, warned curbing the DNI's power will "diminish its effectiveness and reverse many of the important gains we had made since 9/11."
"It is appropriately staffed and resourced," he said in a statement Wednesday night. "Moreover, to propose changing the CIA's operational structure because of loose allegations of politicization -- claims based on nothing more than the agency's willingness to contradict the President-elect's preferred version of events -- would be a mistake of the highest order."
One source said that Retired Lt. Gen. Michael Flynn -- Trump's pick for national security adviser -- has pushed the idea of reigning in the DNI. Flynn was pushed out as director of the Defense Intelligence Agency in 2014, which falls under the DNI's leadership. Flynn clashed with other intelligence officials, including his bosses Mike Vickers, the Pentagon's undersecretary for intelligence, and DNI James Clapper.
The office of the Director of National Intelligence was created in 2004 to help coordinate intelligence between the different agencies, as a response to the Sept 11 terrorist attacks.
The DNI rolled out a reorganization in 2015 that focused on giving more focus to field offices and Intel gathering, grouping analysis and gathering in field hubs for instance.
CNN's Jim Sciutto and Dan Merica contributed to this report.