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.
The semi-finals will played across two legs in the week of 6 January and 3 February, with the final at Wembley Stadium on Sunday, 16 March.
