Manchester City will travel to Goodison Park to take on Everton while United are away to Leicester in the next round of the FA Cup.
Following the conclusion of the fifth round last night which saw Chelsea beat Barnsley and Southampton overcome Wolves at Molineux, the draw for the quarter-finals throws up a number of intriguing ties.
The two stand-out games of the round are undoubtedly the clashes at Goodison Park and the King Power Stadium. With all four teams in excellent form and riding high in the Premier League, they will all fancy their chances of reaching the last four.
Championship outfit Bournemouth, the only non-Premier League side left in the competition, are at home to Southampton.
Last year's losing finalists Chelsea have been drawn to Premier League bottom club Sheffield United in the remaining tie.
Full quarter-final draw:
Everton v Manchester City
Bournemouth v Southampton
Leicester City v Manchester United
Chelsea v Sheffield United
The ties are scheduled to be played over the weekend of March 20th-21st.
***See LIVE FA Cup quarter-final action on eir sport.