The Blues’ third round fixture at home to the Saints was put back a week after various logistical complications, but victory will then see them face Claude Puel's men, who are currently seventh in the Premier League.
The tie will take place during the week commencing October 29, but is likely to be played on Wednesday, October 31, given Everton face Manchester United in the Premier League on the previous Sunday, October 28.
The Blues travel to the East Midlands next Saturday, October 6, to face the Foxes in the Premier League.
Leicester beat Fleetwood Town and Wolverhampton Wanderers to make it to the fourth round.
The Toffees have never won this competition in their 140-year history, but have twice been runners-up, to Aston Villa in 1977 and against Liverpool in 1984.
Their run in the tournament last season lasted until this stage, when they suffered a fourth round 2-1 defeat at Chelsea in October.