The Italy international signed for PSG on a free transfer in July after failing to come to an agreement with boyhood club Milan over a new contract.
He was one of a number of additions at the Parc des Princes during the transfer window, the highest-profile of which undoubtedly being Messi's arrival from Barcelona.
PSG already had fellow superstar forwards Neymar and Mbappe in its ranks and the duo, along with Messi, have helped Donnarumma develop both on and off the field.
"Training with them makes you improve a lot. Sometimes there are battles that make you grow," he said.
"Training with all these champions helps you develop as a human and as a player.
"It's a good challenge for me. I'm happy to train with them and grow, to move forward in this new challenge of mine. I always try to give my best."
Donnarumma has started PSG's last two matches and now appears to be Mauricio Pochettino's first choice, with Keylor Navas as back-up.
The 22-year-old was previously sharing goalkeeping duties with Navas but insists he did not fear losing his place in the Italy side as a result of his lack of regular minutes.
"That's not a problem," he said. "I went to PSG to play. It's normal that it's like this at the beginning. I'm sure everything will be great.
"I have no problems with the national time. I'm continuing on my path and hope everything will go well for me."
Despite his young age, Donnarumma has already appeared 218 times in Serie A and Ligue 1 combined since making his Milan debut aged 16 in October 2015.
Only Samir Handanovic (219) and Inaki Williams (220) have featured more regularly in Europe's top five leagues across that period.
Donnarumma has kept 72 clean sheets in those 218 league games and has a save percentage of 72.72.
Eleven others to have played at least 100 times in that timeframe rank higher in that metric than Donnarumma, with Atletico Madrid's Jan Oblak (78.87) leading the way.
Donnarumma, who is set to start Italy's Nations League semi-final with Spain on Wednesday, therefore believes there is still room for further improvement.
"There's always a way to learn and get better," he said. "My target is to go higher and higher. There's always something to learn from the goalkeeper coach.
"We try to understand what I need to work on and improve. There's an excellent relationship between us. We try to structure the training in the best possible way.
"With the new coaches, there's a different comparison and this makes me happy for my growth."
Italy confirmed on Monday, meanwhile, that injured Atalanta midfielder Matteo Pessina has been replaced in their 23-man squad by Federico Dimarco for this week's Nations League Finals.