Liverpool have been paired with Champions League holders Barcelona in the draw for the last 16.
The last two winners of the Champions League meet in the last 16
The first leg will be played at the Nou Camp as Liverpool try to repeat their 2005 Champions League triumph.
Jose Mourinho will have to guide Chelsea past Porto, where he won the trophy in 2004, while Manchester United will take on French outsiders Lille.
Celtic face Italian giants AC Milan, while last season's runners-up Arsenal play PSV Eindhoven.
Chelsea, Manchester United and Arsenal will have the benefit of playing their second leg games at home after finishing top of their groups.
Scottish champions Celtic will hope their outstanding home form in the competition so far will establish a platform for progress before their second leg in the San Siro.
Liverpool club secretary Bryce Morrison claimed the pairing with reigning champions Barcelona could be the launch pad for another assault on Europe's top prize for the five-times winners.
This is a competition we've never won before and we're determined to win it
Arsenal vice-chairman David Dein
Morrison said: "They don't come much bigger than that. We are relishing these games. We hope we can go all the way once again, starting with this big one."
Barcelona director Josep Cubells said: "It's an interesting match to play Liverpool the champions of Europe the year before.
"Both are legendary clubs with very glamorous stadiums and enthusiastic supporters."
Manchester United face a Lille team whose results against them in the group stage last season contributed to the English club's early elimination from the competition.
But manager Sir Alex Ferguson told the club website: "We had a bad experience last year but this is a different United team.
"It is an emerging team, which is getting better all the time. We know it will be a difficult tie but we have improved so much from last season."
Arsenal boss Arsene Wenger believes the key to beating PSV Eindhoven is the first leg in Holland.
Wenger said: "This tie will be a lot harder than some people expect it to be. PSV are a good team who qualify for the knock-out stage most years and they're top of the league in Holland.
"We learned from Bayern Munich and Real Madrid last season that the way you play the first leg will often decide who goes through."
PSV coach Ronald Koeman claimed Arsenal have the advantage, with the second leg at the Emirates stadium.
Koeman told his club's website: "Arsenal are not the hardest team, but also not the weakest opponents.
"If you had the choice you would rather play the second leg at home as it is the decisive game. But the consequence of finishing second in the group is that we were not in a position to choose."
Chelsea winger Arjen Robben admitted the Blues might have landed a tougher prospect than manager Jose Mourinho's former club Porto.
We will be reasonably confident in front of our own supporters
Celtic chief executive Peter Lawwell
Robben said: "It could have been worse with the likes of Real Madrid and Inter Milan in that group, those are the two toughest teams.
"At this stage of the competition you would never get an easy draw and if you are going to win the Champions League you have to beat teams like Porto.
"It's a nice draw for the manager, the staff and players like Paulo Ferreira and Ricardo Carvalho.
Two former winners, Real Madrid and Bayern Munich, will play each other with a quarter-final place at stake.
Gerard Houllier's French champions and dark horses Lyon will face AS Roma, while Inter Milan play talented Spanish side Valencia.
Celtic chief executive Peter Lawwell told BBC Radio Scotland: "AC Milan are a formidable club who, by their own standards, are having a difficult time. Although I'm sure the injury situation will be cleared by February.
"But we will be reasonably confident in front of our own supporters."
Porto v CHELSEA
CELTIC v AC Milan
PSV Eindhoven v ARSENAL
Lille v MANCHESTER UNITED
Roma v Lyon
Barcelona v LIVERPOOL
Real Madrid v Bayern Munich
Inter Milan v Valencia
(Ties to be played on 20/21 February and 6/7 March)