The Premier League sides all completed their group stage fixtures last week, with Chelsea and United finishing as group winners. As a result, they will face the runners-up from the other groups, but cannot face another English side at this stage of the competition.
The Gunners and City, who finished second in their respective groups, could potentially face the cream of European football, with both Barcelona and Real Madrid possible opponents for Arsene Wenger and Manuel Pellegrini's sides.
The first knockout stage will be played over two legs, with the first of which being on February 18 and 19 or a week later February 25 and 26. The return legs will then be played a fortnight later to decide which teams make it to the last eight.
The quarter-finals will then take place on April 1 and 2, and April 8 and 9, while the semi-finals will be held on April 22 and 23, with the return fixtures to be played on April 29 and 30.
The final, which will be played at Estadio do Sport Lisboa e Benfica, is on Saturday May 24.Uefa general secretary Gianni Infantino will be in charge of proceedings for the draw in Switzerland, which are set to start at 11am GMT.
Arsenal's potential opponents: Atletico Madrid, Barcelona, Bayern Munich, Real Madrid, Paris St Germain.
Chelsea's potential opponents: AC Milan, Bayer Leverkusen, Galatasaray, Olympiakos, Zenit St Petersburg.
Manchester City's potential opponents: Atletico Madrid, Barcelona, Borussia Dortmund, Real Madrid, Paris St Germain.Manchester United's potential opponents: AC Milan, Galatasaray, Olympiakos, Schalke, Zenit St Petersburg.