League leaders United take on Reading tomorrow evening, while a week on Wednesday Chelsea will travel to Middlesbrough.
Should both emerge victorious, they will then meet at Old Trafford on the weekend
of Saturday, March 9.
Elsewhere in the draw, champions Manchester City have been paired with Barnsley, while there will be an all-Championship meeting between Millwall and Blackburn Rovers in South London.
The final tie will see the winners of the replay between Oldham Athletic and Everton play host to Wigan Athletic.