The Italian had just completed 10 years of service in Turin, but injury and poor form had left him doubting his future at La Vecchia Signora.
However, Buffon was convinced to stay at Juventus and is now more committed than ever to helping the club succeed.
"The phone rang and it was Antonio Conte. I expected it. He told me important things," Buffon told Gazzetta dello Sport.
"In the previous season, the first of president Andrea Agnelli, in the first half of the season I didn't play due to injury and in the second half I wasn't very good.
"My mind was elsewhere. I thought it might be the moment to change, to quit Juve. I met the new officials and they changed my mind. That phone call was so important and from that moment on I've been a Juve fan even more than I was before."
Buffon joined Juve from Parma in 2001.