Roberto Martinez’s men progressed to the last eight with a 2-0 win at Bournemouth on Saturday, while Chelsea cruised to a 5-1 victory against a young Manchester City side at Stamford Bridge on Sunday.
The last-eight clash is a repeat of the 2009 final in which Louis Saha opened the scoring for Everton after 25 seconds, only for goals from Frank Lampard and Didier Drogba to turn the match in Chelsea’s favour.
Chelsea’s current interim boss Guus Hiddink was also in charge for that match.
West Ham’s reward for a 5-1 win at Blackburn is a trip to Shrewsbury or Manchester United, who go head to head in the fifth round on Monday night.
Arsenal will play Watford at the Emirates Stadium if the Gunners can get past Hull in a fifth-round replay at the KC Stadium.
Ties to be played March 11-14.
Draw in full
Reading v Crystal Palace
Everton v Chelsea
Arsenal or Hull v Watford
Shrewsbury or Manchester United v West Ham