Everton will face Sheffield Wednesday in the FA Cup fourth round.
The winner of another fourth round tie involving Tottenham Hotspur or Wycombe has then been scheduled to take place against the victor in the Blues' clash at Goodison Park.
The fifth round tie would take place at Goodison once again.
Carlo Ancelotti's men beat Championship side Rotherham 2-1 in the third round of the competition and secured progression after goals from Cenk Tosun and Abdoulaye Doucoure.
The fourth round ties are due to be played around the weekend of January 23/24, with the fifth round set to take place in midweek, on Wednesday, February 10.
The Football Association announced that there would be a double draw on Monday, January 11, with the fourth-round draw immediately followed by the draw for the fifth round.
It marked a change in the traditional approach but was done to "aid fixture scheduling" in this most unusual of seasons, due to the ongoing coronavirus pandemic, and followed a similar organisation by the EFL in the Carabao Cup earlier this season.
Everton were allocated number 10 for the draw.
