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Holders Liverpool will visit Premier League strugglers Southampton.
Arsenal host Crystal Palace in a London derby, while Newcastle United are at home to Brentford.
The quarter-final ties will take place in the week of 16 December.
It is the first time in 14 years there have been no EFL clubs in the League Cup quarter-finals.
Spurs beat Manchester City in the fourth round, while United – who beat Leicester 5-2 under interim boss Ruud van Nistelrooy – will hope to have Ruben Amorim in charge by then.
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