Bayern Munich, who knocked out Celtic in the last round, face Bundesliga rivals Bayer Leverkusen in the last 16.
Aston Villa, who secured the final automatic spot in the last 16, will face Belgian side Club Brugge.
If Arsenal can overcome PSV, they will face the winners of the Madrid derby between Real and Atletico in the last eight.
Liverpool and PSG last met in the group phase in 2018-19, the year the Reds went on to win the trophy for the sixth time.
The last 16 first legs will be played on the evenings of 4 and 5 March, with the return legs on 11 and 12 March.
