The 22-year-old only joined PSG in July after reaching the end of his Milan contract and failing to agree fresh terms with his boyhood club.
However, according to reports from Italy this week, Donnarumma is already eyeing up a move to Juventus in January as he is not happy about having to challenge Keylor Navas for a starting spot.
Donnarumma was given an extended break after playing a huge part in Italy's Euro 2020 success and had to wait until six games into the campaign to make his debut in a 4-0 Ligue 1 win over Clermont.
He has played a further two games since – the 2-1 league win over Lyon and 2-0 victory over Manchester City in the Champions League on Tuesday – compared to eight appearances for Navas in all competitions.
But after being given the nod to start the big game with City, Donnarumma dismissed reports he is unwilling to share goalkeeping duties with Navas
"I laugh at it," he said when asked about the recent speculation. "Every time I open the phone, I read a lot of it.
"I know my strength, I know who I am and there is no problem whatsoever. I am here, and I am happy to be here.
"I have a club that always supports me, and I just laugh when I read all this nonsense. I'm fine, and I'm going to continue."
Donnarumma impressed on his Champions League debut for PSG by making seven saves at the Parc des Princes, as goals from Idrissa Gueye and Lionel Messi earned the hosts a deserved win.
"I dreamed of a night in the Champions League like this," Donnarumma said. "It was a great match and gives me immense joy.
"I thank all the people who have been close to me, from my parents to my girlfriend. It hasn't been an easy time, but I have an incredible family. I knew this moment would come.
"Playing with these champions is fantastic, they help you a lot and make you grow. Congratulations to Leo as well for his first goal. He is a phenomenon – there's nothing more to say."
Mauricio Pochettino must now decide whether to stick with Donnarumma in goal for Sunday's league trip to Rennes or instead turn to Navas.
Navas has conceded eight goals in his eight appearances for PSG this campaign, compared to one goal shipped in three outings for Donnarumma, who also boasts a better save percentage (92.86 compared to 75.76).
Donnarumma's save percentage of 92.86 is the best of any player from Europe's top five leagues to have played at least three times across all competitions, with Arsenal's Aaron Ramsdale (91.67) and Chelsea's Edouard Mendy (88.89) next on the list.