Pep Guardiola's side have made the competition their own in recent seasons, winning each of the last three renewals and five of the last seven.
City made a belated return to Premier League action at Wolves on Monday night and were impressive as last year's PFA Player of the Year Kevin de Bruyne inspired a 3-1 win against a side that had become a bogey team.
Bournemouth, meanwhile, have made a solid start to life in the Championship following their relegation last season and the departure of long-time manager Eddie Howe. The Cherries have taken four points from their first two league games and reached this stage of the competition via a remarkable 11-10 penalty shootout win over Crystal Palace in round two.
A fourth round meeting with Burnley at Turf Moor lies ahead for the winners after the Clarets beat Millwall on Wednesday.
The match has not been selected for live broadcast on UK television.
With no fans allowed inside stadiums due to the Rule of Six regulations, supporters can tune in from home by accessing the Carabao Cup Live Streaming platform.
Individual passes cost £10 and this offer applies to any game involving a Premier League club which is not chosen for live TV coverage.