LaLiga giant Barca became the first team in the competition's history to overturn a 4-0 first-leg deficit when it famously defeated PSG 6-1 in the return tie at the same stage in the 2016-2017 season.
Neymar scored twice and assisted Sergi Roberto's last-gasp winner on that occasion but his status to face his former club with PSG may be in doubt after the Brazil superstar sustained a serious-looking ankle injury in Monday's (AEDT) 1-0 loss at Lyon.
Barca also defeated PSG in the quarter-finals en route to treble glory in 2014-2015 and in the last eight in the 2012-2013 campaign.
PSG was runners-up in a competition delayed by the coronavirus pandemic last term, and its conqueror Bayern was paired against Serie A side Lazio.
Meanwhile in the Europa League, Manchester United have been drawn against Real Sociedad in the Europa League, while Arsenal will face Benfica in the last 32 of the competition.
Leicester City will be on the road for the first leg of their tie with Slavia Prague, while Milan will have to get past Red Star Belgrade if they want to remain on course to lift the only European trophy that has eluded the club so far.
Steven Gerrard's Rangers go up against Royal Antwerp, Roma face Braga and Napoli will take on Granada.
As for Ajax, who finished third in a Champions League group that included Liverpool and Atalanta, the Dutch club have been drawn with Lille.