Italian Donnarumma signed from AC Milan last summer to join veteran Navas, 35, who has been in the French capital since leaving Real Madrid in 2019.
Despite stressing his "very good relationship" with Navas, Donnarumma insisted it was out of the question to share the job next season.
"No, I think it will surely not happen like that, because I think the club will make choices," Donnarumma told AFP in an interview.
"We're two good guys, we understand the situation, but it was hard, and for him too, but let's say that we managed it well."
Donnarumma said "yes of course" he wanted to stay next season with his contract running until 2026.
The 23-year-old lifted his first league title with PSG, while for Costa Rican Navas it was a second in France to join the La Liga trophy and three Champions League trophies he won in Spain.
"It's beautiful, it's my first league title, I'm very happy, and it's my first trophy with the Paris Saint-Germain shirt," said Donnarumma.
"I'm very proud to belong to a great, very ambitious club, always aiming higher."
Donnarumma arrived in France after being named the best player in the European championships which Italy won.
"The debut was not easy, because it was my first outside Italy, in a new club, a new city (but) pressure, no," explained Donnarumma, who had spent six years in Milan.
"I feel a big family behind me, a big club, the welcome was great, and after it was easier for me."
Donnarumma said it hadn't been an "easy" season, giving it seven out of 10.
"I know I can do more," he said. "I haven't played so many matches, only half, that wasn't easy. In the conditions I experienced, I couldn't give the maximum, but I'm convinced that I can give a lot more to this team and this club."
In addition to PSG's Champions League exit to Real Madrid in the last 16, Donnarumma's Italy failed to qualify for a second straight World Cup.
"It was hard, very hard," he sighed.
"The following days were very difficult, but there is no going back. What we did at the Euro will remain in history, we have achieved something incredible.
"Unfortunately we did not succeed in going to the World Cup, but we have to look ahead and start again."