The former US First Daughter signed a three-month deal with NBC in November to highlight inspiring news stories for the network's 'Making a Difference' segments.
Clinton debuted on NBC in December with a report on an Arkansas non-profit group for Brian Williams's primetime news show Rock Centre.
NBC and Clinton are now close to reaching an agreement to extend the 31-year-old's contract, sources have told The Washington Post.
Clinton will apparently remain a correspondent for Rock Centre if a further contractual agreement can be reached.
The length of Clinton's possible new deal with NBC has not yet been revealed.
Clinton is also currently pursuing her doctorate in Public Health at New York University.
Last year, Clinton spoke out in support of same-sex marriage at a benefit for the social networking website Friendfactor.
"I certainly believe that all of my friends, as [husband] Marc [Mezvinsky] and I did, should have the right to marry their best friends," she said at the time.