The English duo were the last pair out in Friday's quarter-final draw in Nyon, which also saw holders Real Madrid given a tie against Juventus, last season's beaten finalists who knocked out Tottenham.
Anfield will host the first leg of the quarter-final tie, which will be played on April 4 with the second leg to be held on April 10 at the Etihad Stadium.
The two English clubs have already played each other twice in the Premier League this season.
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 leaders City, who were beaten 4-3 with two late goals adding some respectability to the final scoreline.
Here is a look back at five memorable Champions League clashes between English rivals...
Chelsea v Arsenal 2003-04 (Chelsea won 3-2 on aggregate)
Roman Abramovich's money was beginning to bear fruit for Chelsea and they were paired with Arsenal in an all-London quarter-final.
The Gunners, on their way to winning the Premier League without losing a game, assumed the ascendancy after getting out of Stamford Bridge with a 1-1 draw.
Jose Antonio Reyes then gave them a half-time lead in the second leg at Highbury but a brilliant Chelsea fightback began with a Frank Lampard goal just after the restart and ended in thrilling fashion with Wayne Bridge's 87th-minute winner.
Chelsea v Liverpool 2004-05 (Liverpool won 1-0 on aggregate)
Jose Mourinho's Chelsea were paired against Rafael Benitez's Liverpool in the semi-finals to guarantee an English team would be in Istanbul for the final.
After a goalless first leg at Stamford Bridge, it all came down to the return match at Anfield that still rankles among Chelsea fans.
Luis Garcia's fourth-minute goal decided the contest, but it was shrouded in controversy as replays showed William Gallas cleared the ball before it crossed the line.
The goal stood and Liverpool went on to beat AC Milan in thrilling fashion.
Man Utd v Chelsea 2007-08 (Man Utd won on penalties)
Sir Alex Ferguson lifted a second Champions League crown, nine years after his first, as Manchester United turned Moscow red in the final against Chelsea.
Cristiano Ronaldo headed United in front, only for Frank Lampard to draw Avram Grant's Chelsea level before the break.
There were no other goals and the game was decided on penalties. The shoot-out will be remembered for John Terry's slip, when a goal would have won it for Chelsea, but it was Edwin van der Sar's save from Nicolas Anelka that proved decisive.
Chelsea v Liverpool 2008-09 (Chelsea won 7-5 on aggregate)
Gus Hiddink's side won the away leg of the quarter-final 3-1 but Liverpool gave them an almighty scare at Stamford Bridge, surging into a two-goal lead at half-time.
Didier Drogba, Alex and Frank Lampard bagged in the second half to put Chelsea back in control before a frantic final 10 minutes.
Lucas Leiva and Dirk Kuyt struck in the space of two minutes to leave Liverpool needing just one more goal to seal a sensational win, only for Lampard to make the game safe in the 89th minute.
Man Utd v Arsenal 2008-09 (Man Utd won 4-1 on aggregate)
Only long-time rivals Arsenal stood in front of Manchester United and a second successive Champions League final and the tie was in the balance as United headed to the Emirates Stadium for the second leg with a slender 1-0 lead.
But they enjoyed a dream start in London as Park Ji-Sung and Cristiano Ronaldo put United 2-0 up after only 11 minutes. Ronaldo added a second in the second half, meaning the contest was over by the time Robin van Persie scored a late penalty.
Additional reporting by the Press Association.