The Whites avoided the division’s top teams in tonight’s draw but will face top flight opposition for the first time this season after yesterday’s 2-1 win at Bolton Wanderers.
United are due to visit Vicarage Road over the weekend of February 20.
Their Championship clash away at Birmingham City - planned for the same date - is set to be rescheduled.
Watford came through round four of the FA Cup with a 1-0 win at Nottingham Forest yesterday.
Leeds are bidding to reach the last eight of the tournament for the first time in 13 years.