Dembele's first year at Borussia Dortmund was also a huge success and both players are tipped to be the subject of massive transfer bids this summer.
Pogba, who is the most expensive footballer in history following his €105 million move to Man Utd last year, expects big things from the pair if they can keep their wits about them.
"The young players like Mbappe and Dembele are very talented," Pogba told Telefoot. "I've never seen this, young players imposing themselves like that, being relaxed like that.
"Mbappe and Dembele have the future before them, they must be serious. They're kids, young people who have a brain. I wish them the best, also with France."
Goal understands Mbappe, 18, could be subject to a world-record €135m bid from Monaco's French rivals Paris Saint-Germain, although Champions League winners Real Madrid are widely expected to attempt to sign him too.
According to Le Journal du Dimanche, Monaco are willing to give Mbappe a 900 per cent wage rise in an effort to persuade him to stay at the principality club.
Both teenagers are expected to be part of France's World Cup 2018 squad, which will undoubtedly be one of the favourites should they reach the finals.
However, Didier Deschamps' side fell out of Group A's automatic qualification spot with four games to go following their 2-1 defeat to Sweden earlier this month.
"The qualification table is not the best for France, we wanted to win against Sweden," Pogba, who starred at Euro 2016 as France finished runners up, admitted.
"Everyone wants us to win, we are all responsible against Sweden. We are second, we have to be courageous and take our chances with both hands to go for the top spot."
France host Netherlands at the Stade de France on August 31 in a must-win match for both European giants.
Dick Advocaat's side are three points behind France and Sweden - ahead of their opponents on goal difference - in Group A.