Mbappe, 19, is currently the second highest football transfer ever after completing his €180m (R2.8b) permanent transfer to Paris Saint-Germain from AS Monaco this month.
Despite his tender age, Mbappe has already featured 22 times for the senior France side, scoring eight goals, four of which came in the triumphant Russia 2018 campaign.
And Klose, who scored 16 World Cup goals for Germany from 2002-14 and told Le Parisien that the teenager has everything to equal or even better his records.
"Considering Kylian's age, he should be able to play in four more World Cups," Klose said. "He is likely to equal or better my record.
"To do this, France must remain competitive over that period. Right now, that is looking very likely."
Klose went on to discuss his Ballon d'Or chances, as the World Cup victory could be used as the springboard to the most coveted individual honour dominated by Lionel Messi and Ronaldo over the past decade.
"Logically, Kylian will be one of the main candidates," Klose said.
"However, he will have some big competition from his teammate Griezmann, the best player of the World Cup Modric and Champions League winner Ronaldo.
"Many things can happen between now and October, though."
Mbappe has scored 38 goals and registered 31 assists in 104 senior football apperances for Monaco and PSG respectively.