Manchester United will also notably play at home to 2022 Europa League runners-up Rangers and go to Portugal to play Porto, another of Jose Mourinho's old sides.
Olympiakos will face Fiorentina in the Europa Conference League final after making history with their 2-0 win against Aston Villa in Thursday's semi-final second leg.
Olympiakos showed no signs of nerves in their first ever European semi-final with Ayoub El Kaabi taking his tally for the season to 30 goals.
West Ham's 17-match unbeaten European run came to an end on Thursday with a 2-1 loss away to Olympiakos.
Arsenal reached the Europa League quarterfinals despite losing 0-1 to Olympiakos in the 2nd leg while Dinamo Zagreb knocked out Tottenham Hotspur after extra time.
Simon Kjaer's last-gasp equaliser gave AC Milan a dramatic 1-1 draw at Manchester United, handing the Italians a great chance of reaching the Europa League quarter-finals.
Kostas Tsimikas agreed a five-year contract with Liverpool and is expected to provide back-up for first choice left-back Andy Robertson at Anfield.
Wolves battled into the quarter-finals of the Europa League on Thursday while Sevilla, Bayer Leverkusen and Basel enjoyed far more comfortable victories in the matches that brought the Europa League round of 16 to a belated close.
The final between Olympiakos and AEK Athens was originally scheduled for July 26 but the former refused to play at a smaller stadium in Rizoupoli instead of the Athens Olympic Stadium.
Pierre-Emerick Aubameyang scored with a sensational bicycle kick and had a chance to seal the tie with the final kick of the game, but somehow fired wide from six yards out.
Ajax, Celtic, Benfica and Porto went out but Manchester United hardly broke sweat after Simon Deli of Brugge conceded a penalty and earned a red card in the 23rd minute at Old Trafford and won 5-0.
Manchester United will take on Club Brugge in the last 32 of the Europa League while struggling Arsenal will face Greek side Olympiakos.
Champions League: Jose Mourinho was quick to acknowledge the ball boy's contribution to Harry Kane's first goal against Olympiacos FC as he went up straight to him and shook hands with him.
The incident prompted the Olympiakos team to leave the pitch in protest before riots erupted outside the ground.
The Greek league match between hosts Panathinaikos and arch-rivals Olympiakos was delayed after home fans clashed with police before the game and threw flares at Olympiakos players.
Thomas Mueller, who has been in tremendous form, netted twice while Mario Goetze also struck a goal to help FC Bayern Munich beat Olympiakos 3-0 in their Champions League match.
Bayern Munich will look to repeat their 2013 triple of Champions League, Bundesliga and German Cup titles.