The Premier League pace-setters faced the Toffees at the same stage of the competition two years ago, with Virgil van Dijk scoring a late winner on his Reds debut to seal a 2-1 victory.
Meanwhile, Manchester United have been drawn against Wolves – the side who advanced to the semi-finals of the famous tournament at their expense back in March.
Leeds will travel to Arsenal in another mouthwatering tie, while holders Manchester City face Port Vale at the Etihad stadium.
All 32 third-round ties, which will take place over the weekend of January 3-6, will kick-off one minute later than usual.
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