The last-eight draw in Nyon saw Nick Cushing's City side handed a two-leg clash against Swedish champions Linkoping, while Chelsea boss Emma Hayes saw her team paired with French outfit Montpellier.
The tie of the round sees holders Lyon tackle Spanish giants Barcelona, which is set to see England internationals Lucy Bronze and Toni Duggan go head to head.
Both left Manchester City in the summer to move abroad, with right-back Bronze joining French club Lyon and striker Duggan heading to Barcelona.
German side Wolfsburg will play Czech team Slavia Prague, and the winner of that contest will face Chelsea or Montpellier in the semi-finals.
If Manchester City overcome Linkoping, they will play Lyon or Barcelona for a place in the final. City lost 3-2 on aggregate to Lyon in the last four last season.
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