Zverev reached his fourth Grand Slam title clash by beating Czech 26th seed Jakub Mensik 7-5, 6-2, 3‑6, 6-3 on Friday, shortly before 10th seed Cobolli advanced when fellow Italian Matteo Arnaldi withdrew due to a viral illness.
Looking ahead to the final, where he will seek his maiden major trophy, Zverev struck a respectful tone when discussing his opponent's family.
"We got closer at the Laver Cup in 2024 in Berlin," Zverev told reporters.
"Sometimes when there were difficult moments, his father used to come up to me and would ask me questions. He would ask my father questions about tennis, about different things.
"I was always very happy to talk to him. I think that's when it started. With some people it just continues naturally, and it does with Flavio."
The mutual respect has carried into their rivalry, which stands at 3-1 to Zverev after he gained revenge in the Madrid quarter-finals for a loss to Cobolli in the semis in Munich.
"He's a great player and a great guy," Zverev added.
"I look forward to playing him in the final. Of course, it's his first final, I'm happy for him that he reached it. But yeah, the only thing I can control is that I play good tennis. I'll try to show my level.
"I'll try to do the right things. That's the only thing that matters to me."
'I could play again now'
Zverev said Cobolli being fresher by not playing his semi-final would have no bearing on the final.
"I feel fine. I didn't have brutally long matches. I feel like I could play again now," Zverev said.
"I think it's not the way that you want a semi-final of a Grand Slam to happen, but I also saw Matteo in the locker room, and he looked awful. I understand it.
"There's nothing much he can do. Things like that happen. We're all human. We don't wish for them to happen, but they do. I don't think it's going to be a big difference on Sunday."
After losing last year's Australian Open final, his third defeat in the title round on the biggest stage, Zverev said he had no difficulty staying calm in the months that followed.
"It's not been that long. It was last year," Zverev added.
"Throughout most of the time I was either number two or number three in the world. So I do feel like I can get back to those stages, and I do feel like I'll get back to the stages throughout the entire period.
"I didn't play well last year ... but I felt like I was going to find it again. I'm happy to be back at this stage."