The German revealed that, when at recent grands prix it was only rumoured that McLaren's Hamilton was considering the switch, he spoke in the paddock with the 2008 world champion.
"We were laughing about it," Rosberg told reporters at Suzuka.
"Because we spoke about it when we were 14 years old in go-karts. 'Ah, imagine if, one day, we're teammates in F1, how cool would that be?' Well, now all of a sudden it's happening, which is quite unreal," he said.
"I didn't necessarily talk him into it," Rosberg insisted.
"I tried to stay quite objective. Yes, I mentioned the positives and he asked a few things and I gave honest answers. My answers are all positive because I am positive of the team."