Both campaigns say a final deal hasn’t yet been reached and the Democratic National Committee hasn’t signed off on the agreement.
But the New Hampshire debate Thursday would give Clinton and Sanders a high-profile encounter before the nation’s first presidential primary.
The agreement was first reported by BuzzFeed.
Clinton and Sanders are in a tight race before Monday’s Iowa caucuses, and Clinton trails the Vermont senator in New Hampshire.
Clinton has urged the party to add the media forums while Sanders has been willing to appear at the proposed debate next week in exchange for the three later dates.