Premier League champions Manchester City face German side RB Leipzig, while Tottenham play Italian giants AC Milan.
Chelsea also have German opposition in Borussia Dortmund.
Elsewhere, French champions Paris St-Germain have drawn Bayern Munich.
The last-16 first legs will take place on 14-15 and 21-22 February, with the second legs on 7-8 and 14-15 March.
A historic rivalry meets again
Two of those occasions have been in finals, with Real Madrid winning both in 2017-18 and 2021-22.
The Spanish champions also knocked Liverpool out in the quarter-finals in the 2020-21 season.
Jurgen Klopp’s side have been in three of the last five European finals, including last season’s in Paris, and only AC Milan and Real Madrid have won the competition more times.
The organisation of the Reds’ final defeat in Paris was later described as “an abject failure” by European football’s ruling body Uefa after fans were robbed and tear-gassed outside the Stade de France and kick-off was delayed by 36 minutes.
More than 480 testimonies by supporters and journalists at the 28 May final were examined by an independent panel, which included Professor Phil Scraton, who previously led a report into the 1989 Hillsborough stadium disaster.
Full last-16 draw:
RB Leipzig v Manchester City
Club Bruges v Benfica
AC Milan v Tottenham
Frankfurt v Napoli
Borussia Dortmund v Chelsea
Inter Milan v Porto
Paris St-Germain v Bayern Munich