The pair were karting team mates as teenagers but their relationship famously became strained during the three years they battled for the championship as Mercedes team mates.
Now Rosberg hopes the pair can repair their relationship following his decision to quit F1 less than a week after winning the championship last month.
"We had a few nice conversations since my retirement. There were some kind words from him," he told BBC Sport.
"Who knows, in the future, we might get on well again."
The pair have been rivals for much of their racing lives, something which Rosberg says makes his triumph over Hamilton all the more special.
"Beating Lewis makes it all the more special because he is one of the best out there, a great rival and a very, very tough competitor," he said. "I just went all out this year."
Bahrain International Circuit - Winter testing