City qualified for the quarter-finals with a 3-1 win over Premier League side Crystal Palace. 

United, meanwhile, comfortably disposed of Swansea City on their way to the last eight. 

The tie will take place at Bristol City's home ground, giving them a better chance of knocking out the defending champions. 

Meanwhile, Brad Smith's AFC Bournemouth will take on Chelsea at Stamford Bridge. 

In the other two quarters, Arsenal host London rivals West Ham, and Leicester City welcome Manchester City to the King Power Stadium. 

The ties will be played in the week starting December 18.