The Italy goalkeeper left PSG over the summer to join City. He and Haaland share the same agent.
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"When I had the opportunity to come here, he (Haaland) wrote to me. He pushed for me to come here, and I am very grateful for that," Donnarumma tells Sky Sports.
"He is a really good friend - and it's good that I play with him, because it's very difficult to play against him. He is an alien."
Donnarumma is happy with his start at City, and grateful to his teammates.
"I didn't expect to have such a positive impact in the Premier League straight away," he added.
"But the team has helped me a lot. From the moment I arrived here I have felt very welcome."