Bayern are in a strong position to make the quarterfinals, having beaten Chelsea 3-0 at Stamford Bridge in the first leg, while Barca's tie is much more finely balanced, following their 1-1 draw at Napoli.
Manchester City secured an impressive 2-1 win away to Real Madrid and will look to finish the job off at the Etihad, and they will face the winners of the clash between Lyon and Juventus, with the French side having won the first meeting 1-0.
Should Juve exit against Lyon, Cristiano Ronaldo would be in line for his first round-of-16 exit in 10 years.
Because of the unprecedented stoppage brought upon by the global coronavirus pandemic, the tournament will be formed of one-off matches in Lisbon from the quarterfinal stage onward, with the four remaining round-of-16 second legs to take place on Aug. 7 and 8.
The quarterfinals will be played from Aug. 12 to 16, the semifinals on Aug. 18 and 19 and the final on Aug. 23.
Istanbul was originally planned to host the 2020 final and will now host the 2021 final.
Meanwhile, City are set to learn their fate over their involvement in next season's Champions League, with a decision on their appeal over their two-year ban expected next week.
City were handed a two-year suspension from European club competitions and a €30 million fine by UEFA in February after being found guilty of breaching financial fair play regulations.
Alongside the draw for the men's tournament, the UEFA executive committee also announced it would allow the clubs left in the Women's Champions League to register six new players for the quarterfinals onwards.
"All six players may have been fielded for another club in a previous round, but only a maximum of 3 can have played for another quarter-finalist," a statement posted on social media said.
Round-of-16 ties still to be concluded:
Chelsea (0) vs. Bayern Munich (3)
Napoli (1) vs. Barcelona (1)
Real Madrid (1) vs. Manchester City (2)
Lyon (1) vs. Juventus (0)
Quarterfinals (to be played Aug. 12-16)
There are no seedings or country protection for the draw.
Real Madrid/Manchester City vs. Lyon/Juventus
RB Leipzig vs. Atletico Madrid
Napoli/Barcelona vs. Chelsea/Bayern Munich
Atalanta vs. Paris Saint-Germain
Semifinals (to be played Aug. 18-19)
Real Madrid/Manchester City or Lyon/Juventus vs. Napoli/Barcelona or Chelsea/Bayern Munich
RB Leipzig or Atletico Madrid vs. Atalanta or Paris Saint-Germain