Pep Guardiola’s side could secure an unprecedented quadruple this season but they will need to overcome a Chelsea side who remain unbeaten in all competitions since Thomas Tuchel took charge in January.
City, who were eliminated at the semifinal stage last season, edged past Everton on Saturday with a 2-0 win.
Chelsea, who were beaten finalists last year, beat Sheffield United by the same scoreline on Sunday.
Southampton cruised into the FA Cup semifinal with a 3-0 victory over Bournemouth on Saturday and could meet Manchester United at Wembley in a repeat of the 2017 League Cup final. Southampton have suffered 9-0 Premier League defeats against both United and Leicester City in the last 18 months.
If Leicester manage to get past United, they will have the chance to reach their first FA Cup final since 1969 and win the competition for the first time in their history.
Both games will be played at Wembley on the weekend of April 17 and 18.
Draw in full:
Leicester or Manchester United vs. Southampton
Chelsea vs. Manchester City