Manchester United's FA Cup quarter-final tie with holders Arsenal will be shown live on BBC One.
The tie will be played on Monday, 9 March at 19:45 GMT.
The BBC's other live game involves Tim Sherwood's Aston Villa, who face West Midlands rivals West Bromwich Albion at 17:30 on Saturday, 7 March.
BT Sport are showing Bradford City against Reading at 12:45 on 7 March and Liverpool v Blackburn Rovers on Sunday, 8 March at 16:00.
The Bradford game will be free for non-BT subscribers to watch, on its website or on BT Sport 1.
Their road to the quarter-finals this season included comfortable victories over Hull and Middlesbrough, though Brighton gave them a scare in a 3-2 win in the fourth round.
Manchester United came from behind to beat League One side Preston 3-1 at Deepdale on Monday having beat League One Yeovil and League Two Cambridge United - the latter after a replay.
All three of Villa's wins this year have come in the FA Cup. Sherwood watched from the stands as his new charges beat Leicester City 2-1 in the fifth round, after they accounted for Championship sides Blackpool and Bournemouth.
The Baggies might be struggling in the Premier League, but they have been impressive in the FA Cup, the most notable performance being a 4-0 win against West Ham at The Hawthorns in the fifth round.
League One side Bradford are into the quarter-finals of the FA Cup for the first time since 1976. They hope to progress further against Reading after following up an astonishing 4-2 win at Chelsea in the fourth round with another top-flight scalp in beating Sunderland 2-0 at Valley Parade in the fifth round. Striker Jon Stead has scored in all five rounds so far.
Reading have picked up a hat-trick of victories on the road to fellow Championship sides Huddersfield, Cardiff City and Derby County.
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 (3-1) and Stoke (4-1) already this season.
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.