Mbappe, 19, became the second teenager to score in a World Cup final as he helped fire France past Croatia last month.
The other man to achieve the feat, Pele, joked he would have to "dust off he boots" if the explosive young forward continued to threaten his records.
Italy legend Buffon says his new team-mate can finish a burgeoning career among football's very finest, recalling a first-hand experience of Mbappe's immense potential in the 2016-17 Champions League semi-finals.
The then-Monaco man capped a startling breakthrough season by beating Buffon for his side's only goal in a 2-1 second-leg defeat in Turin.
"When I spoke [after the match] with Andrea Barzagli, who is one of my great friends, he told me 'Gigi, in 20 years of my career I have rarely seen a player run so fast with the ball, I had a hard time stopping him'," the goalkeeper told PSG's official club magazine.
"These words are not insignificant because Barzagli, when he is focused and fit, is really a top defender.
"It's obvious [Mbappe] has something more than others. I hope he will remain humble and keep this desire to progress and make sacrifices.
"If so, he will make a mark in the history of football and write incredible pages of the sport."
Mbappe returned to PSG on Monday following an extended post-World Cup break.