Liverpool suffered locally this season, as they needed penalty kicks to beat Derby County, the second-tier rival, on Wednesday, after a goalless draw at Anfield.
Manchester City, who have won four of the last five titles, had to work hard to beat Chelsea in the third round.
City’s only defeat in all competitions this season was against Liverpool, where the goal of Egyptian Mohamed Salah near the end gave Liverpool a 1-0 win in the league last month.
Manchester United, who came from behind twice to beat Aston Villa 4-2 at Old Trafford, host second-tier Burnley in the fourth round.
There is another pure confrontation between two Premier League teams that will bring together Newcastle United and Bournemouth.
The matches will be played in the week that begins on December 19, immediately after the World Cup final.
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