The Champions League quarter-final draw will take place in Switzerland at 11:00 GMT on Friday - and be immediately followed by the semi-final draw.
Liverpool and Manchester City are in the draw, with Chelsea joining them after beating Atletico Madrid.
There are no restrictions on who could be drawn against who.
The Europa League quarters and semis draws will take place at 12:00 GMT with Premier League sides Arsenal and Manchester United involved.
In the Champions League, Bayern Munich, Borussia Dortmund, Paris St-Germain, Porto and Real Madrid are the other sides through.
After the draws for the quarters and semis, a draw will decide the 'home' side in the final - which is at Ataturk Olympic Stadium in Istanbul - for administrative reasons.
The quarter-finals will take place on 6-7 and 13-14 April.
Who is through to Champions League quarter-finals?
Bayern Munich and Borussia Dortmund from Germany, English sides Chelsea, Liverpool and Manchester City, Paris St-Germain of France, Portuguese side Porto and Spain's Real Madrid.
What are the Europa League draw details?
The draw for the quarter-finals of the Europa League will be made at 12:00 GMT on Friday, after the Champions League draw.
There are no restrictions on which teams can face each other.
The semi-final draw will take place afterwards, as will the draw to see who is officially 'home' in the final in Gdansk, Poland.
The last-eight matches are on 8 and 15 April.
Which British sides are in the draw?
Only two of the four British sides competing in the round of 16 made it through to the quarters - Arsenal and Manchester United.
Arsenal lost 1-0 to Olympiakos in their second leg but went through courtesy of their 3-1 win in the first leg in Greece.
A Paul Pogba goal gave United a 1-0 second-leg win over AC Milan, sealing a 2-1 aggregate victory over the Italian side.
Tottenham took a 2-0 lead to Croatia to face Dinamo Zagreb but were stunned as a Mislav Orsic hat-trick swung the tie away from them, the winning goal coming in extra time.
Rangers had both Kemar Roofe and Leon Balogun sent off as they lost 2-0 to Slavia Prague at Ibrox, giving the Czech side a 3-1 aggregate win.
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