FA Cup holders Arsenal will travel to Manchester United in the quarter-finals next month.
United confirmed their place in the last eight after coming from behind to win 3-1 at Preston North End.
The Gunners, who beat Hull City in last year’s final, defeated Middlesbrough in the fifth round.
Liverpool host Blackburn, League One survivors Bradford City face Reading while West Midlands rivals Aston Villa and West Brom will meet at Villa Park.
Liverpool’s last-eight draw will give Steven Gerrard hope of reaching Wembley in his final season at the Reds, although they will have to overcome a Blackburn side who have knocked out Premier League opposition in Swansea and Stoke already this season.
League One side Bradford are into the quarter-finals of the FA Cup for the first time since 1976, and will be confident of progressing further after beating Premier League sides Chelsea and Sunderland in the previous rounds.
The quarter-final draw was made by England boss Roy Hodgson and Brian Finney, son of Preston legend Tom Finney, at Deepdale on Monday before the Preston-Manchester United game.
The draw in full:
Liverpool v Blackburn Rovers
Bradford City v Reading
Manchester United v Arsenal
Aston Villa v West Brom
Ties to be played on 7 and 8 March.