The Magpies booked their place in the draw with a 3-1 third round win over Luton Town on Saturday, and their reward is a trip to either Carrow Road or Stamford Bridge.
The tie between Norwich and Chelsea finished goalless at the weekend, with a replay set for Wednesday, 17th January to decide who will host the Magpies in the next round.
Should the Canaries prevail in the replay, it would mean United's Jacob Murphy could line up against his twin brother Josh, a winger for the Championship side.
A win for Chelsea, meanwhile, would mean a return to Stamford Bridge for former Blues boss Rafa Benítez.
The fourth round tie is due to be played on the weekend of Saturday, 27th January and Sunday, 28th January, but is subject to change, should it be selected for television coverage.
Further details regarding the tie will be confirmed in due course.