Jurgen Klopp’s men were drawn against Premier League leaders City with Anfield hosting the first leg on April 3. The second leg to be held on April 10.
Klopp is in confident mood ahead of the clash and said: “It is exactly like it was before – we take what we’ve got. Now it’s Manchester City, let’s go.
“We’ve lost once and we’ve won once against them in the league – and I don’t think they thought before the best draw they could have got is Liverpool. That’s a sign for us and how strong we can be.
“We are for sure not the favourites in this round, but in the last eight there are not a lot of favourites – maybe two of them, Bayern and Barcelona – but thank God it’s football and nothing is decided.
“We have a few games to play until then, but I am really looking forward to it and we will give it everything.”
There are six days separate the two legs and, sandwiched in between them, is Manchester City’s crunch Premier League clash with Manchester United.
Klopp said: “In this case, it’s not too important. For us, it’s completely normal. We can get a result at home for sure, but it’s obviously a difficult game – but good news for both teams.
“It is like it is should be in the last eight. It was clear we would face a strong team. Now we have Man City. The good thing is they are the team we know most about.
“It’s not too cool for England because now only one team can go to the semis. But we will try everything.”
City secured their place in the last eight by beating Basel, having won the away leg 4-0, but then lost 2-1 at home in the second leg.
Liverpool saw off Porto in the round of 16, which also saw an impressive away performance with a 5-0 victory at the Estadio do Dragao ahead of a routine goalless draw at Anfield.
Anfield will host the first leg of the quarter-final tie, which will be played on April 3 or 4 with the second leg to be held on April 10 or 11.
Elsewhere in Friday’s quarter-final draw, holders Real Madrid were handed a tie against Italian giants Juventus, who beat Tottenham in the last round.
La Liga leaders Barcelona will play Roma, while the reward for Sevilla’s victory over Manchester United was a date against Bayern Munich of Germany.
The two English clubs have already played each other twice in the Premier League this season.
Manchester City romped to a 5-0 home win during September, with Gabriel Jesus and Leroy Sane both scoring twice after Sadio Mane had been sent off.
Liverpool, though, gained revenge at Anfield in January when they inflicted what so far has been the only Premier League defeat for City, who were beaten 4-3 with two late goals adding some respectability to the final scoreline.