Navas started his second season with the Parisian club as one of the 7 club players to test positive for COVID-19. He missed the clubs first two games due to the quarantine requirement. On 16 September 2020, Navas played his first game of the season winning and keeping a clean sheet against Metz. On 17 September, UEFA announced Navas, for the second time, as a nominee for the 2019–20 Champions League Goalkeeper of the Season award. On 20 September, Navas starred in PSG's 0–3 away win to Nice with a second consecutive clean sheet as well as several excellent saves. On 13 January 2021, Navas won the 2020 Trophée des Champions. With that win, he became the CONCACAF player with the most European trophies, 16, surpassing former FC Barcelona and international Mexican defender Rafael Márquez. On 20 April 2021, Navas was voted Ligue 1 Player of the Month for March, making him the first CONCACAF player to win the award.