Mbappe has shone at the World Cup in Qatar, where he is currently the top scorer, and netted twice against Poland in the last-16 to become the youngest player to reach five knockout-stage goals at the tournament since Pele in 1958.
Giroud became France’s all-time record goalscorer during the win over Poland, overtaking Thierry Henry, but he is convinced that 23-year-old Mbappe will leapfrog him one day.
“Kylian is one of the best players that I am playing with,” said Giroud. “He is amazing and he’s still young, which is scary because he can still improve his game.
“But he is very efficient and, since the beginning of the competition, he has been crucial for us and he is very decisive, very competitive.
“Obviously, if I can say, he is the best striker that I have ever played with, of all the teams that I have played with.
“But I don’t think we have seen the best of Kylian, I hope and I think. I hope he will improve and I hope he will beat all the records. I know mine will be broken probably by him. I think he is unbelievable.”
Saturday’s quarter-final is a special one for Giroud given he spent nine years playing in England for Arsenal and Chelsea. France goalkeeper Hugo Lloris is in a similar boat, having joined Tottenham in the same summer Giroud moved to Arsenal (2012).
England players celebrate their FIFA World Cup 2002 Round of 16 victory over Senegal
The pair have been discussing facing England and Giroud has said that both he and Lloris are desperate not to lose given their ties to the Premier League.
“So far they (England) have had a great tournament and I think they will have a tough game on Saturday,” Giroud added. “I know very well this team and we were talking with Hugo Lloris, regarding this game, and we said we don’t want to lose against England! It’s a really special game for us.
“We are really excited about this game, so many great players from young generations. They have quality and got lots of different options. It will be a nice game to watch I think, very interesting. But I hope it is going to go well for us.”