Mbappe has been in stunning form in recent weeks and became the youngest player to make his France debut in over 60 years on Saturday when featuring against Luxembourg.
The striker has been linked with a string of Europe's leading clubs, including Chelsea, and current Blues forward Costa has been impressed by the 18-year-old.
Costa said of Mbappe in an interview with Telefoot: "If he continues to progress at this speed… he is a phenomenon.
"He is fast, a killer in front of goal, he is very strong. He has his feet on the ground, people say, and he has his head on his shoulders. I hope he will continue like that."
Meanwhile, ahead of Spain's friendly against France at the Stade de France on Tuesday, Costa believes Les Bleus should end Karim Benzema's international exile.
Benzema has not represented his country since being investigated in relation to an alleged attempt to blackmail his international team-mate Mathieu Valbuena.
The French Football Federation suspended the 29-year-old, causing him to miss Euro 2016 on home soil.
FFF president Noel Le Graet has since stressed France boss Didier Deschamps is free to select the player but Benzema, who denies any wrongdoing in the blackmail case, was omitted once again for the current round of international fixtures.
"I do not know what really happened, but Benzema is still Benzema," Costa added.
"Not to summon him is to lose a big benchmark on a global level – when he's good, he's one of the best.
"Players want to participate in the big tournaments. For the good of football, he should be there. I love this player."
Nevertheless, Chelsea's top scorer is also a fan of the attacking talent Deschamps has at his disposal.
Mbappe's emergence sets up the tantalising prospect of the Monaco sensation being paired with Antoine Griezmann, who has taken up Costa's former mantle as Atletico Madrid's attacking talisman.
"The French team proved during the last Euro that it was very strong, they have very big players. At the same time, they are young," he said.
"Griezmann is really a great player, exceptional. He is one of the best in the world.
"There is also [N'Golo] Kante, who I play with for my club. This France team has a collective even more dangerous than its individuals."