The match will be played week commencing 21 December.
City will be hoping to avenge last July’s 2-0 FA Cup semi-final against the Gunners as Pep Guardiola again locks horns with his protégé Mikel Arteta.
The teams last met in the Carabao Cup in 2018 when City beat Arsenal 3-0 in the final at Wembley.
It will be the ninth meeting in the League Cup between the clubs.
The Gunners were unbeaten in the first five, but City have won the last three meetings without conceding a goal.
City are looking for a record-equalling fourth successive triumph in a competition the Club has excelled in over the past decade.
Liverpool won the League Cup four times on the bounce between 1981 and 1984.
The full quarter-final draw is:
Stoke City v Spurs
Brentford v Newcastle United
Arsenal v Manchester City
Everton v Manchester United
Fixture details will be released in due course.
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