Arsenal will face Paris St-Germain in the Women's Champions League quarter-finals while Glasgow City take on two-time European champions Wolfsburg.
If Women's Super League champions Arsenal get past PSG, then holders and six-time European title winners Lyon could await in the last four.
Lyon, who are aiming to win a fifth Champions League in a row, face Bayern Munich in the quarters.
Atletico Madrid, who eliminated Manchester City, next face Barcelona.
Arsenal, the only British side to win European football's top women's club competition, face a difficult path to the final against France's two biggest clubs with the draw, which was made in Switzerland on Friday.
It is the second successive season that the draw has presented such a path for an English side, with Chelsea getting past PSG before being narrowly beaten by Lyon at the semi-final stage last term.
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Glasgow, who edged out Danish side Brondby on penalties to reach the last eight, will be looking to reach the semi-finals for the first time.
The first legs of the quarter-finals will be played on 24-25 March 2020 before the return legs on 1-2 April.
This season's final will be held in Austria's capital Vienna on 24 May.
Women's Champions League quarter-final draw
Arsenal v Paris St-Germain
Glasgow City v Wolfsburg
Atletico Madrid v Barcelona
Lyon v Bayern Munich
Arsenal/Paris St-Germain v Lyon/Bayern Munich
Glasgow City/Wolfsburg v Atletico Madrid/Barcelona
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