Eight-time winners Chelsea will play quadruple-chasing Manchester City in the FA Cup semi-finals.
Leicester and Manchester United know they will face Southampton in the last four if they can earn victory in their quarter-final on Sunday.
Leicester and United were drawing 1-1 when the semi-final draw was made at half-time at the King Power Stadium.
The semi-finals will take place on the weekend of 17-18 April at Wembley, with the final at the same venue on 15 May.
The final could be played in front of 20,000 fans because it has been earmarked as one of the proposed pilot events to test the return of big crowds to UK venues this year.
Leicester/Manchester United v Southampton
Chelsea v Manchester City
How the teams got to the semi-finals
Chelsea are aiming to go one better than last season when they lost to Arsenal in the FA Cup final.
The Blues continued their impressive start under recently-appointed manager Thomas Tuchel with a hard-fought semi-final win over Sheffield United earlier on Sunday.
City, who are aiming to win a quadruple of Premier League, FA Cup, League Cup and Champions League, reached the semi-finals when late goals from Ilkay Gundogan and Kevin de Bruyne earned a 2-0 win at Everton on Saturday.
Southampton cruised into the last four – for the second time in four seasons – with a 3-0 win at Championship side Bournemouth, putting their recent troubles in the Premier League to one side.
Prospective semi-final opponents Manchester United and Leicester have both thrashed Southampton 9-0 within the past two seasons.