The Whites, who made it to the Capital One Cup quarter-finals before being eliminated by Chelsea, drew 1-1 with Birmingham on Saturday to set up a rematch.
Spurs players Aaron Lennon, Andros Townsend and Jake Livermore have all played for the Elland Road outfit at some point during their respective careers.
The fourth-round tie will be played on the weekend of 26/27 January.
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