Sunderland, meanwhile, the only non-Premier League side left in the competition, travel to Arsenal.
West Ham, who beat Spurs in the Premier League last week, reached the last eight of the tournament after knocking out Manchester City. Pep Guardiola's side had won the tournament in each of the last three years.
The ties will be played on Dec. 21 and 22 and broadcast live on ESPN.
Draw in full:
Tottenham Hotspur vs. West Ham United
Arsenal vs. Sunderland
Brentford vs. Chelsea
Liverpool vs. Leicester City