City will face the Championship outfit over two legs and have been drawn at home first, with the Robins visiting the Etihad Stadium on Tuesday 9 January.
Pep Guardiola’s men head to Ashton Gate for the decider two weeks later, on Tuesday 23 January.
Both games will be shown live on Sky Sports and kick off at 7.45pm
This will be the second time the two sides have met in the League Cup, with City victorious in a 2007 encounter thanks to goals from Emile Mpenza and Rolando Bianchi.
While City beat Leicester on penalties to reach the final four, Lee Johnson’s side avoided extra-time and the lottery of a shoot-out when Korey Smith struck in injury time to hand the Robins a 2-1 win over Manchester United.
Ticket information for both the home and away leg will be released on mancity.com in due course.
