Both clubs faced each other at the same stage of the 2018-19 campaign where United progressed to the quarterfinals after a stunning result at the Parc de Princes.
PSG avenged their elimination last season when they secured a 3-1 win at Old Trafford as United were knocked out of the competition during the group stages.
Ronaldo is seeking to win his sixth Champions League trophy and his second at United while Messi has won the competition four times.
Messi also picked up a record-seventh Ballon d’Or trophy last month while Ronaldo has won the award five times during his career.
Bayern enjoyed a perfect winning record in the group stages while Atletico progressed to the round-of-16 with a dramatic final day win at Porto.
Group winners will be away in the first leg, with ties to be played on Feb. 15, 16 and 22, 23. Return legs will be played on March 8, 9 and 15, 16.
The away goals rule has also been abolished in European tournament knockout ties this season.
The rule, which had been in place since 1965, was used to determine a winner when teams were level on aggregate after a two-legged match. The team that had scored more goals as the away side were awarded the victory. But from now, this will be replaced by extra time and penalties.
UEFA will draw the quarterfinal and semifinal ties on the same day for this season, scheduled for March 18.
The final will take place on Saturday, May 28 at Krestovsky Stadium in Saint Petersburg, Russia.
Benfica vs. Real Madrid
Villarreal vs. Manchester City
Atletico Madrid vs. Bayern Munich
FC Salzburg vs. Liverpool
Inter Milan vs. Ajax
Sporting CP vs. Juventus
Chelsea vs. Lille
Paris Saint-Germain vs. Manchester United