Nyon - Liverpool was paired with Chelsea in the Champions League for the fifth time in five years on Friday, while Barcelona was matched against Bayern Munich in another quarterfinal.
Defending champion Manchester United will face FC Porto, which knocked United out in 2004 when Jose Mourinho was in charge of the Portuguese team and took it all the way to the title.
Arsenal plays Villarreal in a repeat of the 2006 semifinal which the Gunners won before losing to Barcelona in the final.
The first legs will be played April 7-8 and the second legs on April 14-15.
Liverpool and Chelsea have already played each other 22 times in five years in all competitions.
"It's a tough route through but then there are no easy ones," Liverpool chief executive Rick Parry said. "A few of the teams were hoping they'd avoid us."
In the semifinals, Manchester United or Porto will face Villarreal or Arsenal, and Barcelona or Bayern Munich will meet Liverpool or Chelsea.
That sets up the possibility of another all-English final. Manchester United beat Chelsea on penalties in last year's final in Moscow. The two teams, currently first and second in the Premier League, could meet again in Rome on May 27.
Liverpool and Chelsea met in the 2005 semifinals, with the Reds going on to beat AC Milan on penalties in a memorable fightback in the final in Istanbul for their fifth triumph in European football's most prestigious competition.
They also met in the group phase in 2006 and the 2007 semifinals, with Liverpool advancing before losing to AC Milan in the final. Last season, Chelsea beat Liverpool in the semifinals.
Parry relished the possibility of facing Manchester United in the final, especially after Liverpool beat the Red Devils 4-1 at Old Trafford on Saturday.
"We've beaten them twice in the league," he said.
Parry said the Liverpool-Chelsea second leg would be on April 14 to avoid a clash with the 20th anniversary of the Hillsborough disaster on April 15. In 1989, 96 Liverpool fans were crushed to death in a fenced-in standing area of the Sheffield stadium in the FA Cup semfinals.
"We don't want to play on that date, particularly not in England," Parry said.
Barcelona, which leads the Spanish league by six points, has won the European title only twice but the last time was in 2006 when it beat Arsenal. Bayern has won it four times, the last being in 2001.
"That's a heck of a draw, it's something quite extraordinary," Bayern coach Juergen Klinsmann said. "It's a great challenge to be measuring up against the best team in Europe right now."
The first legs of the semifinals will be played April 28-29 and the return legs on May 5-6.
The Manchester United-Porto meeting could bring back unhappy memories for United fans, who recall Mourinho running down the side of the Old Trafford pitch after his team scored a late equalizer to knock the English side out. It was a happy occasion for Vitor Baia, who was the Porto goalkeeper in that title-winning season and now is the club's head of foreign relations.
"We're going up against one of the best clubs in the world but that doesn't mean we'll be giving up," Baia said. "We have something to bring to this game. We have shown our quality and our character by coming this far."