Manchester City were also drawn on the road for their fourth round tie as they will visit either Selhurst Park or the Britannia Stadium, depending on who wins the replay between Crystal Palace and Stoke.
Another EPL side, Tottenham Hotspur, will have to wait until the replays are over to find out where they will be traveling during the weekend of January 26.
Spurs were drawn against the winner of the Leeds United versus Birmingham City replay.
After earning a replay late on Saturday, Manchester United will have a chance to host former player Dimitar Berbatov and Fulham if both clubs win their respective replays against West Ham and Blackpool.
Both Merseyside clubs will once again take to the road in fourth round action.
The Toffees potential fourth round match with Sunderland is just one of three potential all-EPL clashes in the fourth round.
The club who pulled off the biggest upset of the third round, Macclesfield Town, were drawn at home against the winner of the Wigan Athletic versus Bournemouth replay.
All third-round replays will be held either January 15 or 16.
Here is the list of the results from Sunday's fourth-round draw.
Norwich City vs. Luton Town
Oldham Athletic vs. Liverpool
Macclesfield Town vs. Wigan Athletic/Bournemouth winner
Middlesbrough vs. Aldershot Town
Leeds United/Birmingham City winner vs. Tottenham
Crystal Palace/Stoke City winner vs. Manchester City
West Ham United/Manchester United winner vs. Fulham/Blackpool winner
Southend United/Brentford winner vs. Chelsea
Reading vs. Sheffield United
QPR/West Brom winner vs. Sheffield Wednesday/MK Dons winner
Bolton/Sunderland winner vs. Everton
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