The semi-final draw, conducted following Liverpool's 2-1 victory over Stoke City at Anfield, also opened up the possibility of a Merseyside derby in the last four.
Liverpool will play the winners of the replay between Everton and Sunderland after the two Premier League sides drew 1-1 at Goodison Park on Saturday.
The match between Spurs and Bolton at White Hart Lane was abandoned on Saturday evening after Bolton midfielder Fabrice Muamba collapsed and suffered a cardiac arrest in the first half.
He remains in a critical condition at The London Chest Hospital and football united in support of the former England Under-21 international on Sunday when players applauded prior to kick-off in the two FA Cup sixth-round ties and both Premier League fixtures.
Either Tottenham or Bolton will play Chelsea in the last four after the London side defeated Leicester City 5-2 at Stamford Bridge.
Liverpool manager Kenny Dalglish told ITV: "The people on Merseyside have two clubs they can be proud of. They [Everton] have a difficult game going to Sunderland to try and get themselves through; we are there and whoever you were going to get was going to be really difficult.
"If it's a Merseyside one fine, but it's a difficult hurdle for Everton to go to Sunderland."
The semi-final ties will be played at Wembley over the weekend of April 14 and 15.