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 hoping to join them after playing 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 Arsenal, Tottenham, Manchester United and Rangers hoping to be involved.
In the Champions League, Paris St-Germain, Borussia Dortmund, Porto and Real Madrid are the other sides already through.
Chelsea lead Atletico Madrid 1-0 from the first leg with Bayern Munich 4-1 up on Lazio. The second legs are on Wednesday at 20:00 GMT.
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
Borussia Dortmund, Liverpool, Paris St-Germain, Porto, Manchester City, Real Madrid
Who can join them?
Winner of Bayern Munich v Lazio on Wednesday – Bayern lead 4-1 from the first leg
Winner of Chelsea v Atletico Madrid on Wednesday – Chelsea lead 1-0 from the first leg
When is Europa League draw?
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 who could be drawn against who.
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 could be in the draw?
Half of the teams in the draw could be British if all four teams come through their last-16 second legs on Thursday.
Arsenal host Olympiakos after winning the first leg 3-1, while Tottenham take a 2-0 lead to Dinamo Zagreb.
Manchester United visit AC Milan having drawn 1-1 at Old Trafford and Rangers host Slavia Prague at Ibrox with the same scoreline.
Roma, Ajax and Villarreal are among the other sides left.