Guus Hiddink’s side face a tough test as they head to Goodison Park, while Arsenal and Manchester United will both play at home should they make it through their fifth round ties
Chelsea will play Everton in the quarter-finals of the FA Cup while Arsenal will face Watford should they see off Hull City in a fifth round replay.
The winner of Monday night’s tie between Manchester United and Shrewsbury Town will take on West Ham, who thrashed Blackburn Rovers in the fifth round.
Guus Hiddink’s side eased into the last eight with a 5-1 win over Manchester City at Stamford Bridge but will be away from home when they take on Roberto Martinez’s Toffees in a rematch of the 2009 final, which was won by the Blues during the Dutchman’s first spell in charge.
Arsenal drew 0-0 with Hull City at the Emirates Stadium on Saturday and have again been handed a home draw against Watford if they beat Steve Bruce’s side in their fifth round replay at the KC Stadium.
Alan Pardew, meanwhile, will return to Reading with his Crystal Palace side who are in the quarter-finals for the first time in 21 years after beating Tottenham at White Hart Lane.
The ties will be played between 11-14 March