FA Cup holders Wigan will travel to runners-up Manchester City in this season's quarter-finals, while Arsenal will host Everton.
Ben Watson's late goal gave Wigan a historic triumph over City in last year's final at Wembley and Manuel Pellegrini's side will be hoping to avenge this defeat at the Etihad Stadium.
Everton, meanwhile, will go to Arsenal after they progressed with a 3-1 win over Swansea at Goodison Park.
Goals from Lacina Traore, Leighton Baines and Steven Naismith sealed Everton's victory before Arsenal beat Liverpool 2-1 in the late kick-off at the Emirates courtesy of goals from Alex Oxlade-Chamberlain and Lukas Podolski, Steven Gerrard scoring the visitors' consolation from the penalty spot.
There is the possibility of a Sheffield derby in the last eight after United beat Nottingham Forest 3-1 on Sunday, but Wednesday must first come through their tie against Charlton.
In the other quarter-final, Sunderland boss Gus Poyet could be heading back to Brighton if his former employers defeat Hull City in Monday's fifth-round clash.
Poyet left Brighton in acrimonious circumstances following the club's play-off second-leg defeat against Crystal Palace.
Arsenal v Everton
Brighton or Hull City v Sunderland
Sheffield United v Sheffield Wednesday or Charlton Athletic
Manchester City v Wigan